16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T477,{"@context":"https://schema.org","@type":"Quiz","name":"Ap Eapcet 2024 Probability PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/ap-eapcet/questions/2024/mathematics/probability/m977diq8","educationalLevel":"Entrance exam preparation","about":"Ap Eapcet / Mathematics / Probability","hasPart":{"@type":"Question","name":"Ap Eapcet 2024 Probability PYQ with Solution","text":"If X \\sim B(5, p) is a binomial variate such that P(X=3)=P(X=4), then P(|X-3|<2)=","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"Given that X \\sim B(5, p) is a binomial random variable and P(X=3) = P(X=4) , we can equate the probabilities: \\Rightarrow { }^5C_3 p^3 (1-p)^2 = { }^5C_4 p^4 (1-p) Calculating each term: The binomial coefficient for X=3 is { }^5C_3 = \\frac{5!}{3!2!} = 10 The binomial coefficient for X=4 is { }^5C_4 = \\frac{5!}{4!1!} = 5 Equating and simplifying the expression: 10 p^3 (1-p)^2 = 5 p^4 (1-p) \\Rightarrow 2(1-p) = p \\Rightarrow 2 - 2p = p \\Rightarrow 3p = 2 \\Rightarrow p = \\frac{2}{3} Thus, p = \\fr..."}}}18:T55a,

Given that $ X \sim B(5, p) $ is a binomial random variable and $ P(X=3) = P(X=4) $, we can equate the probabilities:

$ \Rightarrow { }^5C_3 p^3 (1-p)^2 = { }^5C_4 p^4 (1-p) $

Calculating each term:

The binomial coefficient for $ X=3 $ is ${ }^5C_3 = \frac{5!}{3!2!} = 10$

The binomial coefficient for $ X=4 $ is ${ }^5C_4 = \frac{5!}{4!1!} = 5$

Probability

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