Question 11 Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is atleast one defective egg.Let X : be the number of defective eggs Picking eggs with replacement is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here, n = number of eggs picked = 10 p = Probability of getting defective egg = 10% = 10/100 = 1/10 q = 1 – p = 1 – 1/10 = 9/10 Hence, P(X = x) = 10Cx (𝟏/𝟏𝟎)^𝒙 (𝟗/𝟏𝟎)^(𝟏𝟎 − 𝒙) We need to find Probability that there is atleast one defective egg P(atleast one defective egg) = 1 – P(getting 0 defective eggs) = 1 – P(X = 0) = 1 – 10C0(1/10)^0 (9/10)^(10 −0) = 1 – 1 × 1 × (9/10)^10 = 1 – (9/10)^10

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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