{"id":5517,"date":"2026-10-09T12:30:10","date_gmt":"2026-10-09T07:00:10","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=5517"},"modified":"2026-10-09T12:30:11","modified_gmt":"2026-10-09T07:00:11","slug":"cat-2026-probability-cheat-sheet","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/cat-2026-probability-cheat-sheet\/","title":{"rendered":"CAT 2026 Probability Cheat Sheet: Formulas &amp; Shortcuts"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Stuck on probability questions in CAT mock tests? You&#8217;re not alone.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probability looks tricky, but it&#8217;s actually one of the most formula-driven topics in CAT Quantitative Aptitude. With the right <strong>CAT 2026 Probability Cheat Sheet<\/strong>, you can solve 80% of questions in under 2 minutes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This guide gives you <strong>every probability formula, shortcut, and trick<\/strong> you need for CAT 2026\u2014plus solved examples, common mistakes to avoid, and a quick-revision table. Whether you&#8217;re targeting IIMs or other top B-schools, this cheat sheet will save you hours of revision time.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Why Probability Matters in CAT 2026<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">CAT 2026 is scheduled for <strong>November 29, 2026<\/strong>, with <strong>22 questions in the QA section<\/strong> (66 marks total). While probability falls under <strong>Modern Maths<\/strong> (alongside Permutation &amp; Combination, Set Theory), it typically contributes <strong>1\u20132 questions<\/strong> per paper.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>But here&#8217;s the catch<\/strong>: Probability questions often act as <strong>tie-breakers<\/strong> in high-scoring papers. A single correct answer can push your percentile from 98 to 99+.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Also Read: <a href=\"https:\/\/www.catmock.com\/blog\/cat-quant-shortcuts-tricks\/\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">CAT Quant Shortcuts &amp; Tricks: Topic-Wise Methods to Save Time<\/mark><\/a><\/strong><br>                   <strong><a href=\"https:\/\/www.catmock.com\/blog\/cat-qa-syllabus-the-complete-breakdown\/\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">CAT QA Syllabus \u2013 The Complete Breakdown<\/mark><\/a><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">QA Section Breakdown (CAT 2026)<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Section<\/th><th>Total Questions<\/th><th>Marks<\/th><th>Time<\/th><\/tr><\/thead><tbody><tr><td>VARC<\/td><td>24<\/td><td>72<\/td><td>40 min<\/td><\/tr><tr><td>DILR<\/td><td>22<\/td><td>66<\/td><td>40 min<\/td><\/tr><tr><td><strong>QA<\/strong><\/td><td><strong>22<\/strong><\/td><td><strong>66<\/strong><\/td><td><strong>40 min<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Modern Maths (including Probability)<\/strong>: ~5\u20138% weightage in QA, roughly <strong>1\u20132 questions<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">The Ultimate CAT 2026 Probability Cheat Sheet<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Basic Probability Formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The foundation of every probability question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mtext>Number&nbsp;of&nbsp;Favorable&nbsp;Outcomes<\/mtext><mtext>Total&nbsp;Number&nbsp;of&nbsp;Possible&nbsp;Outcomes<\/mtext><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>S<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = \\frac{\\text{Number of Favorable Outcomes}}{\\text{Total Number of Possible Outcomes}} = \\frac{n(E)}{n(S)}<\/annotation><\/semantics><\/math>P(E)=Total&nbsp;Number&nbsp;of&nbsp;Possible&nbsp;OutcomesNumber&nbsp;of&nbsp;Favorable&nbsp;Outcomes\u200b=n(S)n(E)\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Where<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(E)<\/annotation><\/semantics><\/math>P(E) = Probability of event E<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">n(E)<\/annotation><\/semantics><\/math>n(E) = Favorable outcomes<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>S<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">n(S)<\/annotation><\/semantics><\/math>n(S) = Total outcomes in sample space<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: What&#8217;s the probability of getting a head when tossing a coin?<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Head<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>0.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Head}) = \\frac{1}{2} = 0.5<\/annotation><\/semantics><\/math>P(Head)=21\u200b=0.5<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability Range (Boundaries)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Every probability value lies between 0 and 1:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0<\/mn><mo>\u2264<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2264<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0 \\leq P(E) \\leq 1<\/annotation><\/semantics><\/math>0\u2264P(E)\u22641<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = 0<\/annotation><\/semantics><\/math>P(E)=0 \u2192 Impossible event<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = 1<\/annotation><\/semantics><\/math>P(E)=1 \u2192 Certain event<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Quick Tip<\/strong>: If your answer is negative or greater than 1, you&#8217;ve made a calculation error.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. Complement Rule (NOT Event)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of an event <strong>not<\/strong> happening:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>E<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(E&#8217;) = 1 &#8211; P(E)<\/annotation><\/semantics><\/math>P(E\u2032)=1\u2212P(E)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Also<\/strong>: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>E<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(E) + P(E&#8217;) = 1<\/annotation><\/semantics><\/math>P(E)+P(E\u2032)=1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: If probability of rain is 0.3, probability of no rain = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo>\u2212<\/mo><mn>0.3<\/mn><mo>=<\/mo><mn>0.7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1 &#8211; 0.3 = 0.7<\/annotation><\/semantics><\/math>1\u22120.3=0.7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Shortcut<\/strong>: For &#8220;at least one&#8221; questions, use:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>at&nbsp;least&nbsp;one<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>none<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{at least one}) = 1 &#8211; P(\\text{none})<\/annotation><\/semantics><\/math>P(at\u00a0least\u00a0one)=1\u2212P(none)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. Addition Rule (OR Events)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of <strong>A OR B<\/strong> (or both) occurring:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cup B) = P(A) + P(B) &#8211; P(A \\cap B)<\/annotation><\/semantics><\/math>P(A\u222aB)=P(A)+P(B)\u2212P(A\u2229B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Special Case \u2013 Mutually Exclusive Events<\/strong> (A and B cannot happen together):<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cap B) = 0<\/annotation><\/semantics><\/math>P(A\u2229B)=0<br>So, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cup B) = P(A) + P(B)<\/annotation><\/semantics><\/math>P(A\u222aB)=P(A)+P(B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: Probability of getting a 2 or 5 on a dice:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>\u222a<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>6<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(2 \\cup 5) = \\frac{1}{6} + \\frac{1}{6} = \\frac{2}{6} = \\frac{1}{3}<\/annotation><\/semantics><\/math>P(2\u222a5)=61\u200b+61\u200b=62\u200b=31\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. Multiplication Rule (AND Events)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of <strong>A AND B<\/strong> both occurring:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>For Independent Events<\/strong> (one doesn&#8217;t affect the other):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cap B) = P(A) \\times P(B)<\/annotation><\/semantics><\/math>P(A\u2229B)=P(A)\u00d7P(B)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>For Dependent Events<\/strong> (one affects the other):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cap B) = P(A) \\times P(B|A)<\/annotation><\/semantics><\/math>P(A\u2229B)=P(A)\u00d7P(B\u2223A)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: Probability of getting two heads in two coin tosses:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>H<\/mi><mo>\u2229<\/mo><mi>H<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(H \\cap H) = \\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{4}<\/annotation><\/semantics><\/math>P(H\u2229H)=21\u200b\u00d721\u200b=41\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">6. Conditional Probability<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of A <strong>given that<\/strong> B has already occurred:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mtext>provided&nbsp;<\/mtext><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo mathvariant=\"normal\">\u2260<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(A|B) = \\frac{P(A \\cap B)}{P(B)}, \\quad \\text{provided } P(B) \\neq 0<\/annotation><\/semantics><\/math>P(A\u2223B)=P(B)P(A\u2229B)\u200b,provided&nbsp;P(B)\ue020=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: A bag has 3 red and 2 blue balls. You draw one ball (it&#8217;s red). What&#8217;s the probability the next ball is also red?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After first red: 2 red, 2 blue left<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Second&nbsp;red<\/mtext><mi mathvariant=\"normal\">\u2223<\/mi><mtext>First&nbsp;red<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>0.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Second red} | \\text{First red}) = \\frac{2}{4} = 0.5<\/annotation><\/semantics><\/math>P(Second\u00a0red\u2223First\u00a0red)=42\u200b=0.5<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">7. Bayes&#8217; Theorem (Reverse Conditional Probability)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Updates probability based on new evidence:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(A|B) = \\frac{P(B|A) \\times P(A)}{P(B)}<\/annotation><\/semantics><\/math>P(A\u2223B)=P(B)P(B\u2223A)\u00d7P(A)\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>When to Use<\/strong>: When you know <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(B|A)<\/annotation><\/semantics><\/math>P(B\u2223A) but need <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A|B)<\/annotation><\/semantics><\/math>P(A\u2223B). Common in CAT questions involving medical tests, quality checks, or multiple scenarios.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: A factory has two machines. Machine A produces 60% of items (5% defective), Machine B produces 40% (10% defective). If a randomly picked item is defective, what&#8217;s the probability it came from Machine A?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.6<\/mn><mo separator=\"true\">,<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(A) = 0.6, P(B) = 0.4<\/annotation><\/semantics><\/math>P(A)=0.6,P(B)=0.4<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Defective<\/mtext><mi mathvariant=\"normal\">\u2223<\/mi><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.05<\/mn><mo separator=\"true\">,<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Defective<\/mtext><mi mathvariant=\"normal\">\u2223<\/mi><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Defective}|A) = 0.05, P(\\text{Defective}|B) = 0.10<\/annotation><\/semantics><\/math>P(Defective\u2223A)=0.05,P(Defective\u2223B)=0.10<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Defective<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.6<\/mn><mo>\u00d7<\/mo><mn>0.05<\/mn><mo>+<\/mo><mn>0.4<\/mn><mo>\u00d7<\/mo><mn>0.10<\/mn><mo>=<\/mo><mn>0.07<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Defective}) = 0.6 \\times 0.05 + 0.4 \\times 0.10 = 0.07<\/annotation><\/semantics><\/math>P(Defective)=0.6\u00d70.05+0.4\u00d70.10=0.07<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mi mathvariant=\"normal\">\u2223<\/mi><mtext>Defective<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mn>0.05<\/mn><mo>\u00d7<\/mo><mn>0.6<\/mn><\/mrow><mn>0.07<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>0.03<\/mn><mn>0.07<\/mn><\/mfrac><mo>\u2248<\/mo><mn>0.428<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(A|\\text{Defective}) = \\frac{0.05 \\times 0.6}{0.07} = \\frac{0.03}{0.07} \\approx 0.428<\/annotation><\/semantics><\/math>P(A\u2223Defective)=0.070.05\u00d70.6\u200b=0.070.03\u200b\u22480.428<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">8. Binomial Probability (Repeated Trials)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For <strong>n independent trials<\/strong> with probability of success <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math>p:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>k<\/mi><mtext>&nbsp;successes&nbsp;in&nbsp;<\/mtext><mi>n<\/mi><mtext>&nbsp;trials<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mi>n<\/mi><mi>k<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u00d7<\/mo><msup><mi>p<\/mi><mi>k<\/mi><\/msup><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow><mi>n<\/mi><mo>\u2212<\/mo><mi>k<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P(k \\text{ successes in } n \\text{ trials}) = \\binom{n}{k} \\times p^k \\times (1-p)^{n-k}<\/annotation><\/semantics><\/math>P(k&nbsp;successes&nbsp;in&nbsp;n&nbsp;trials)=(kn\u200b)\u00d7pk\u00d7(1\u2212p)n\u2212k<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Where<\/strong>: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mi>n<\/mi><mi>k<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><mrow><mi>k<\/mi><mo stretchy=\"false\">!<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>k<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\binom{n}{k} = \\frac{n!}{k!(n-k)!}<\/annotation><\/semantics><\/math>(kn\u200b)=k!(n\u2212k)!n!\u200b (combination formula)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: A coin is tossed 5 times. What&#8217;s the probability of getting exactly 3 heads?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><mo>=<\/mo><mn>5<\/mn><mo separator=\"true\">,<\/mo><mi>k<\/mi><mo>=<\/mo><mn>3<\/mn><mo separator=\"true\">,<\/mo><mi>p<\/mi><mo>=<\/mo><mn>0.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n = 5, k = 3, p = 0.5<\/annotation><\/semantics><\/math>n=5,k=3,p=0.5<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>H<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mn>5<\/mn><mn>3<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>10<\/mn><mo>\u00d7<\/mo><mn>0.125<\/mn><mo>\u00d7<\/mo><mn>0.25<\/mn><mo>=<\/mo><mn>0.3125<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(3H) = \\binom{5}{3} \\times (0.5)^3 \\times (0.5)^2 = 10 \\times 0.125 \\times 0.25 = 0.3125<\/annotation><\/semantics><\/math>P(3H)=(35\u200b)\u00d7(0.5)3\u00d7(0.5)2=10\u00d70.125\u00d70.25=0.3125<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">9. At-Least-One Rule (Compound Trials)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For &#8220;at least one success in n trials&#8221;:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>at&nbsp;least&nbsp;one<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>none<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi>n<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{at least one}) = 1 &#8211; P(\\text{none}) = 1 &#8211; (1-p)^n<\/annotation><\/semantics><\/math>P(at&nbsp;least&nbsp;one)=1\u2212P(none)=1\u2212(1\u2212p)n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: Probability of getting at least one head in 3 coin tosses:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>at&nbsp;least&nbsp;one&nbsp;H<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>0.125<\/mn><mo>=<\/mo><mn>0.875<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{at least one H}) = 1 &#8211; (0.5)^3 = 1 &#8211; 0.125 = 0.875<\/annotation><\/semantics><\/math>P(at&nbsp;least&nbsp;one&nbsp;H)=1\u2212(0.5)3=1\u22120.125=0.875<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">10. Permutation &amp; Combination (P&amp;C) Link<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability questions often need P&amp;C for counting outcomes:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Permutation<\/strong> (arrangement):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mrow><\/mrow><mi>n<\/mi><\/msup><msub><mi>P<\/mi><mi>r<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><mrow><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">^nP_r = \\frac{n!}{(n-r)!}<\/annotation><\/semantics><\/math>nPr\u200b=(n\u2212r)!n!\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Combination<\/strong> (selection):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mrow><\/mrow><mi>n<\/mi><\/msup><msub><mi>C<\/mi><mi>r<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><mrow><mi>r<\/mi><mo stretchy=\"false\">!<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">^nC_r = \\frac{n!}{r!(n-r)!}<\/annotation><\/semantics><\/math>nCr\u200b=r!(n\u2212r)!n!\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example<\/strong>: From 5 boys and 3 girls, what&#8217;s the probability of selecting 2 boys and 1 girl for a team of 3?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total ways: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mn>8<\/mn><mn>3<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>56<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\binom{8}{3} = 56<\/annotation><\/semantics><\/math>(38\u200b)=56<\/li>\n\n\n\n<li>Favorable ways: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u00d7<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mn>3<\/mn><mn>1<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>10<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\binom{5}{2} \\times \\binom{3}{1} = 10 \\times 3 = 30<\/annotation><\/semantics><\/math>(25\u200b)\u00d7(13\u200b)=10\u00d73=30<\/li>\n\n\n\n<li>Probability: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>30<\/mn><mn>56<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>15<\/mn><mn>28<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{30}{56} = \\frac{15}{28}<\/annotation><\/semantics><\/math>5630\u200b=2815\u200b<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Quick-Revision Probability Formula Table<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Concept<\/th><th>Formula<\/th><th>When to Use<\/th><\/tr><\/thead><tbody><tr><td><strong>Basic Probability<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>S<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = \\frac{n(E)}{n(S)}<\/annotation><\/semantics><\/math>P(E)=n(S)n(E)\u200b<\/td><td>All probability questions<\/td><\/tr><tr><td><strong>Complement<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>E<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(E&#8217;) = 1 &#8211; P(E)<\/annotation><\/semantics><\/math>P(E\u2032)=1\u2212P(E)<\/td><td>&#8220;Not E&#8221; or &#8220;at least one&#8221; questions<\/td><\/tr><tr><td><strong>Addition (OR)<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cup B) = P(A) + P(B) &#8211; P(A \\cap B)<\/annotation><\/semantics><\/math>P(A\u222aB)=P(A)+P(B)\u2212P(A\u2229B)<\/td><td>A or B (or both) occurring<\/td><\/tr><tr><td><strong>Mutually Exclusive<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u222a<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cup B) = P(A) + P(B)<\/annotation><\/semantics><\/math>P(A\u222aB)=P(A)+P(B)<\/td><td>A and B cannot happen together<\/td><\/tr><tr><td><strong>Multiplication (AND)<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2229<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>B<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(A \\cap B) = P(A) \\times P(B)<\/annotation><\/semantics><\/math>P(A\u2229B)=P(A)\u00d7P(B)<\/td><td>Independent events both occurring<\/td><\/tr><tr><td><strong>Conditional<\/strong><\/td><td>( P(A<\/td><td>B) = \\frac{P(A \\cap B)}{P(B)} )<\/td><\/tr><tr><td><strong>Bayes&#8217; Theorem<\/strong><\/td><td>( P(A<\/td><td>B) = \\frac{P(B<\/td><\/tr><tr><td><strong>Binomial<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>k<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mi>n<\/mi><mi>k<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><msup><mi>p<\/mi><mi>k<\/mi><\/msup><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mrow><mi>n<\/mi><mo>\u2212<\/mo><mi>k<\/mi><\/mrow><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P(k) = \\binom{n}{k} p^k (1-p)^{n-k}<\/annotation><\/semantics><\/math>P(k)=(kn\u200b)pk(1\u2212p)n\u2212k<\/td><td>Repeated independent trials<\/td><\/tr><tr><td><strong>At-Least-One<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mo>\u2265<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>p<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi>n<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P(\\geq 1) = 1 &#8211; (1-p)^n<\/annotation><\/semantics><\/math>P(\u22651)=1\u2212(1\u2212p)n<\/td><td>&#8220;At least one success&#8221; in n trials<\/td><\/tr><tr><td><strong>Permutation<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><\/mrow><mi>n<\/mi><\/msup><msub><mi>P<\/mi><mi>r<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><mrow><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">^nP_r = \\frac{n!}{(n-r)!}<\/annotation><\/semantics><\/math>nPr\u200b=(n\u2212r)!n!\u200b<\/td><td>Arrangement problems<\/td><\/tr><tr><td><strong>Combination<\/strong><\/td><td><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><\/mrow><mi>n<\/mi><\/msup><msub><mi>C<\/mi><mi>r<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">!<\/mo><\/mrow><mrow><mi>r<\/mi><mo stretchy=\"false\">!<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">!<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">^nC_r = \\frac{n!}{r!(n-r)!}<\/annotation><\/semantics><\/math>nCr\u200b=r!(n\u2212r)!n!\u200b<\/td><td>Selection problems<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Solved CAT-Style Probability Questions<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 1: Basic Probability<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Q<\/strong>: A bag contains 4 red, 5 blue, and 6 green balls. If one ball is drawn at random, what is the probability it is either red or green?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total balls = 4 + 5 + 6 = 15<\/li>\n\n\n\n<li>Favorable (red or green) = 4 + 6 = 10<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;or&nbsp;Green<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>10<\/mn><mn>15<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red or Green}) = \\frac{10}{15} = \\frac{2}{3}<\/annotation><\/semantics><\/math>P(Red\u00a0or\u00a0Green)=1510\u200b=32\u200b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer<\/strong>: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{3}<\/annotation><\/semantics><\/math>32\u200b or 0.67<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 2: Conditional Probability<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Q<\/strong>: Two dice are rolled. Given that the sum is 8, what is the probability that one of the dice shows a 3?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Possible outcomes for sum = 8: (2,6), (3,5), (4,4), (5,3), (6,2) \u2192 5 outcomes<\/li>\n\n\n\n<li>Favorable (one die shows 3): (3,5), (5,3) \u2192 2 outcomes<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>One&nbsp;3<\/mtext><mi mathvariant=\"normal\">\u2223<\/mi><mtext>Sum&nbsp;8<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{One 3} | \\text{Sum 8}) = \\frac{2}{5}<\/annotation><\/semantics><\/math>P(One\u00a03\u2223Sum\u00a08)=52\u200b<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer<\/strong>: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{5}<\/annotation><\/semantics><\/math>52\u200b or 0.4<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 3: Binomial Probability<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Q<\/strong>: A student answers 5 MCQs randomly (each with 4 options). What is the probability of getting exactly 2 correct?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>n<\/mi><mo>=<\/mo><mn>5<\/mn><mo separator=\"true\">,<\/mo><mi>k<\/mi><mo>=<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mi>p<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>0.25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n = 5, k = 2, p = \\frac{1}{4} = 0.25<\/annotation><\/semantics><\/math>n=5,k=2,p=41\u200b=0.25<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac linethickness=\"0px\"><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.25<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.75<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P(2) = \\binom{5}{2} \\times (0.25)^2 \\times (0.75)^3<\/annotation><\/semantics><\/math>P(2)=(25\u200b)\u00d7(0.25)2\u00d7(0.75)3<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>=<\/mo><mn>10<\/mn><mo>\u00d7<\/mo><mn>0.0625<\/mn><mo>\u00d7<\/mo><mn>0.421875<\/mn><mo>=<\/mo><mn>0.2637<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 10 \\times 0.0625 \\times 0.421875 = 0.2637<\/annotation><\/semantics><\/math>=10\u00d70.0625\u00d70.421875=0.2637<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer<\/strong>: ~0.264 or 26.4%<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Question 4: At-Least-One Rule<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Q<\/strong>: A shooter hits the target with probability 0.6. If he fires 4 shots, what is the probability of hitting the target at least once?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>at&nbsp;least&nbsp;one&nbsp;hit<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>no&nbsp;hits<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{at least one hit}) = 1 &#8211; P(\\text{no hits})<\/annotation><\/semantics><\/math>P(at\u00a0least\u00a0one\u00a0hit)=1\u2212P(no\u00a0hits)<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>no&nbsp;hit<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>0.6<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>4<\/mn><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.4<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>4<\/mn><\/msup><mo>=<\/mo><mn>0.0256<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{no hit}) = (1 &#8211; 0.6)^4 = (0.4)^4 = 0.0256<\/annotation><\/semantics><\/math>P(no\u00a0hit)=(1\u22120.6)4=(0.4)4=0.0256<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mo>\u2265<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>0.0256<\/mn><mo>=<\/mo><mn>0.9744<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\geq 1) = 1 &#8211; 0.0256 = 0.9744<\/annotation><\/semantics><\/math>P(\u22651)=1\u22120.0256=0.9744<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer<\/strong>: 0.9744 or 97.44%<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Common Mistakes to Avoid in Probability<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Forgetting to subtract P(A\u2229B)P(A \\cap B)P(A\u2229B) in addition rule<\/strong> \u2192 Leads to double-counting.<\/li>\n\n\n\n<li><strong>Mixing up permutation and combination<\/strong> \u2192 Use permutation for arrangement, combination for selectionbschool.<\/li>\n\n\n\n<li><strong>Ignoring the complement rule<\/strong> \u2192 &#8220;At least one&#8221; is faster as <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>none<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">1 &#8211; P(\\text{none})<\/annotation><\/semantics><\/math>1\u2212P(none).<\/li>\n\n\n\n<li><strong>Assuming events are independent when they&#8217;re not<\/strong> \u2192 Check if one event affects the other.<\/li>\n\n\n\n<li><strong>Not simplifying fractions<\/strong> \u2192 CAT options are often in simplest form.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">How to Use This Cheat Sheet for CAT 2026<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Step 1: Memorize the Core Formulas<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Focus on:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Basic probability <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>n<\/mi><mo stretchy=\"false\">(<\/mo><mi>S<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = \\frac{n(E)}{n(S)}<\/annotation><\/semantics><\/math>P(E)=n(S)n(E)\u200b<\/li>\n\n\n\n<li>Complement rule <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>E<\/mi><mo mathvariant=\"normal\" lspace=\"0em\" rspace=\"0em\">\u2032<\/mo><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(E&#8217;) = 1 &#8211; P(E)<\/annotation><\/semantics><\/math>P(E\u2032)=1\u2212P(E)<\/li>\n\n\n\n<li>Addition and multiplication rules<\/li>\n\n\n\n<li>Conditional probability and Bayes&#8217; theorem<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Step 2: Practice with Timed Mocks<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Solve 10\u201315 probability questions daily under 2-minute limits. Use <a href=\"https:\/\/www.catmock.com\/\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>CAT mock tests<\/strong><\/mark><\/a> to simulate exam pressure.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Step 3: Revise with This Table<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In the last 2 weeks before CAT (November 29, 2026), use the quick-revision table above for daily 5-minute reviews.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Step 4: Link with P&amp;C<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Probability + Permutation &amp; Combination = <strong>2\u20133 guaranteed questions<\/strong> in Modern Maths. Master both together.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Strengthen your P&amp;C skills with <a href=\"https:\/\/www.catmock.com\/bhandara\/70\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">CATMOCK&#8217;s Bhandara<\/mark><\/a> before tackling probability questions.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">FAQs: CAT 2026 Probability Cheat Sheet<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q1: How many probability questions appear in CAT?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Typically <strong>1\u20132 questions<\/strong> from probability (under Modern Maths, which has 5\u20138% QA weightage).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q2: Is Bayes&#8217; theorem important for CAT?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Bayes&#8217; theorem appears in <strong>1\u20132 questions every 2\u20133 years<\/strong>, especially in high-difficulty papers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q3: Should I memorize all formulas or understand concepts?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Both<\/strong>. CAT tests conceptual application, but formula recall saves time. Use this cheat sheet for quick revision.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q4: What&#8217;s the easiest way to solve &#8220;at least one&#8221; probability questions?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Use the <strong>complement rule<\/strong>: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>at&nbsp;least&nbsp;one<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>none<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{at least one}) = 1 &#8211; P(\\text{none})<\/annotation><\/semantics><\/math>P(at\u00a0least\u00a0one)=1\u2212P(none). It&#8217;s faster and reduces calculation errors.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q5: Can I skip probability and focus on Arithmetic instead?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Not recommended. Arithmetic has higher weightage (35\u201340%), but probability questions are <strong>easier to score<\/strong> if you know formulas. Don&#8217;t skip.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Q6: Where can I find official CAT 2026 updates?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Check the <strong>official CAT website<\/strong>: <a href=\"https:\/\/iimcat.ac.in\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>iimcat.ac.in<\/strong><\/mark><\/a> for notifications, admit cards, and exam dates.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Final Thoughts: Master Probability, Boost Your CAT Score<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Probability isn&#8217;t about luck\u2014it&#8217;s about <strong>applying the right formula at the right time<\/strong>. With this <strong>CAT 2026 Probability Cheat Sheet<\/strong>, you now have:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 All essential formulas in one place<br>\u2705 Solved examples matching CAT difficulty<br>\u2705 Quick-revision table for last-minute prep<br>\u2705 Common mistakes to avoid<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Next Step<\/strong>: Download this page, print the formula table, and solve 20+ probability questions from <a href=\"https:\/\/www.catmock.com\/\" target=\"_blank\" rel=\"noreferrer noopener\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>CAT mock tests<\/strong><\/mark><\/a> this week.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remember: CAT 2026 is on <strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">November 29, 2026<\/mark><\/strong>. Every formula you master today is a percentile point gained tomorrow.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You May Also Like :<strong>\u00a0<a href=\"https:\/\/www.catmock.com\/\">CAT MOCK<\/a>,\u00a0<a href=\"https:\/\/www.catmock.com\/pyq\/cat\/2017\">CAT MOCK PYQ<\/a><br><\/strong>Follow Us On :<strong>\u00a0<a href=\"https:\/\/www.facebook.com\/catmock.in?mibextid=ZbWKwL\">Facebook<\/a>,\u00a0<a href=\"https:\/\/www.instagram.com\/cat.mock\">Instagram<\/a>,\u00a0<a href=\"https:\/\/www.youtube.com\/@CATMock\">Youtube<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Stuck on probability questions in CAT mock tests? You&#8217;re not alone. Probability looks tricky, but it&#8217;s actually one of the most formula-driven topics in CAT Quantitative Aptitude. With the right CAT 2026 Probability Cheat Sheet, you can solve 80% of questions in under 2 minutes. This guide gives you every probability formula, shortcut, and trick [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":5523,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5517","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","entry","has-media"],"featured_image_src":"https:\/\/www.catmock.com\/blog\/wp-content\/uploads\/2026\/10\/CAT-2026-Probability-Cheat-Sheet.webp","author_info":{"display_name":"Suesh Pandey","author_link":"https:\/\/www.catmock.com\/blog\/author\/suesh\/"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>CAT 2026 Probability Cheat Sheet: Formulas &amp; 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