Ex 13.5, 3 - There are 5% defective items in a large bulk - Ex 13.5

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Ex 13.5, 3 There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item? Let X : be the number of defective items Picking items is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒﷮𝒏−𝒙﷯ 𝒑﷮𝒙﷯ n = number of items = 10 p = Probability of getting defective item = 5% = 5﷮100﷯ = 1﷮20﷯ q = 1 – p = 1 – 1﷮20﷯ = 19﷮20﷯ Hence, P(X = x) = 10Cx 𝟏﷮𝟐𝟎﷯﷯﷮𝒙﷯ 𝟏𝟗﷮𝟐𝟎﷯﷯﷮𝟏𝟎 − 𝒙﷯ We need to find Probability that we get not more than one defective item P(not more than one defective item) = P(getting 0 defective item) + P(getting 1 defective item) = P(X = 0) + P(X = 1) = 10C0 1﷮20﷯﷯﷮0﷯ 19﷮20﷯﷯﷮10 −0﷯ + 10C1 1﷮20﷯﷯﷮1﷯ 19﷮20﷯﷯﷮10 − 1﷯ = 1 × 1 × 19﷮20﷯﷯﷮10﷯ + 10 × 1﷮20﷯ × 19﷮20﷯﷯﷮9﷯ = 19﷮20﷯﷯﷮10﷯+ 1﷮2﷯ 19﷮20﷯﷯﷮9﷯ = 19﷮20﷯ 19﷮20﷯﷯﷮9﷯+ 1﷮2﷯ 19﷮20﷯﷯﷮9﷯ = 19﷮20﷯﷯﷮9﷯ 19﷮20﷯+ 10﷮20﷯﷯ = 19﷮20﷯﷯﷮9﷯ 29﷮20﷯ = 𝟐𝟗﷮𝟐𝟎﷯ 𝟏𝟗﷮𝟐𝟎﷯﷯﷮𝟗﷯

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