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Last updated at Aug. 11, 2021 by Teachoo
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) 10β1 (B) (1/2)^5 (C) (9/10)^5 (D) 9/10aLet X : be the number of defective bulbs Picking bulbs is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx π^(πβπ) π^π Here, n = number of times we pick a bulb = 5 p = Probability of getting defective bulb = 10/100 = 1/10 q = 1 β p = 1 β 1/10 = 9/10 Hence, P(X = x) = 5Cx (π/ππ)^π (π/ππ)^(πβπ) 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 β0) = 1 Γ 1 Γ (9/10)^5 = (9/10)^5 β΄ Option C is the correct answer