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
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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 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 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 =

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