Ex 13.5, 13

Transcript

Ex 13.5, 13 It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective? In each of the following, choose the correct answer: Let X : be the number of defective articles Picking articles is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒﷮𝒏−𝒙﷯ 𝒑﷮𝒙﷯ n = number of articles = 12 p = Probability of getting defective articles = 10% = 10﷮100﷯ = 1﷮10﷯ q = 1 – p = 1 – 1﷮10﷯ = 9﷮10﷯ Hence, P(X = x) = 12Cx 𝟏﷮𝟏𝟎﷯﷯﷮𝒙﷯ 𝟗﷮𝟏𝟎﷯﷯﷮𝟏𝟐−𝒙﷯ We need to find Probability of getting 9 defective articles out of 12 i.e. P(X = 9) P(X = 9) = 12C9 1﷮10﷯﷯﷮9﷯ 9﷮10﷯﷯﷮12 − 9﷯ = 12 !﷮ 12 − 9﷯ ! 9 !﷯ 1﷮10﷯﷯﷮9﷯ 9﷮10﷯﷯﷮3﷯ = 12 × 11 × 10 × 9 !﷮3 ! 9 !﷯ × 1﷮ 10﷮9﷯﷯ 9﷮10﷯﷯﷮3﷯ = 12 × 11 × 10﷮3 × 2 × 1﷯ × 1﷮ 10﷮9﷯﷯ 9﷮10﷯﷯﷮3﷯= 2 × 11﷮ 10﷮8﷯﷯ 9﷮3﷯﷮ 10﷮3﷯﷯ = 22 𝟗﷮𝟑﷯﷮ 𝟏𝟎﷮𝟖﷯﷯﷯