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Example 32 - Ten eggs are drawn successively from a lot - Examples

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Example 32 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﷯ 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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