Ex 13.5, 14 - Class 12

Transcript

Ex 13.5, 14 In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is (A) 10–1 (B) 1﷮2﷯﷯﷮5﷯ (C) 9﷮10﷯﷯﷮5﷯ (D) 9﷮10﷯ Let X : be the number of defective bulbs Picking bulbs is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒﷮𝒏−𝒙﷯ 𝒑﷮𝒙﷯ n = number of times we pick a bulb = 5 p = Probability of getting defective bulb = 10﷮100﷯ = 1﷮10﷯ q = 1 – p = 1 – 1﷮10﷯ = 9﷮10﷯ Hence, P(X = x) = 5Cx 𝟏﷮𝟏𝟎﷯﷯﷮𝒙﷯ 𝟗﷮𝟏𝟎﷯﷯﷮𝟒−𝒙﷯ We need to find Probability that no bulb is defective i.e. P(X = 0) P(X = 0) = 5C0 1﷮10﷯﷯﷮0﷯ 9﷮10﷯﷯﷮5 −0﷯ = 1 × 1 × 9﷮10﷯﷯﷮5﷯ = 9﷮10﷯﷯﷮5﷯ Option C is the correct answer