# Question 15 (MCQ) - Bernoulli Trial - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Chapter 13 Class 12 Probability

Serial order wise

Last updated at April 16, 2024 by Teachoo

Question 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