Check sibling questions

Ex 13.5, 15 - Probability that student is not a swimmer is 1/5

Ex 13.5, 15 - Chapter 13 Class 12 Probability - Part 2
Ex 13.5, 15 - Chapter 13 Class 12 Probability - Part 3

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Transcript

Ex 13.5, 15 The probability that a student is not a swimmer is 1/5 . Then the probability that out of five students, four are swimmers is (A) 5C4 (4/5)^4 1/5 (B) (4/5)^4 1/5 (C) 5C1 1/5 (4/5)^4 (D) None of theseIf a trial is Bernoulli, then There is finite number of trials They are independent Trial has 2 outcomes i.e. Probability success = P then Probability failure = q = 1 – P (4) Probability of success (p) is same for all trials Let X : be number of swimmers Picking a student is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here, n = number of students = 5 Given probability that student is not a swimmer is 1/5 So, q = 1/5 ∴ p = 1 – q = 1 – 1/5 = 4/5 Hence, P(X = x) = 5Cx (𝟒/𝟓)^𝒙 (𝟏/𝟓)^(𝟓 − 𝒙) We need to find the Probability of that out of five students, four are swimmers i.e. P(X = 4) P(X = 4) = 5C4 (4/5)^4 (1/5)^(5 − 4) = 5C4 (𝟒/𝟓)^𝟒 𝟏/𝟓 = 5C1 𝟏/𝟓 (𝟒/𝟓)^𝟒 Hence, option (A) & (C) both are correct

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.