Ex 13.5, 15 - Chapter 13 Class 12 Probability

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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 these 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﷯ 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