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Question
Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.
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Solution
Let X be the number of defective eggs drawn from 10 eggs.
Then, X follows a binomial distribution with n = 10.
Let p be the probability that a drawn egg is defective.
∴ p = 10% = `1/10`, q = `9/10`
Hence, the distribution is given by
P(X = x) = nCxpxqn−x
P(there is at least one defective egg) = P(X ≥ 1)
= 1 − P(X = 0)
= `1 - ""^10C_0 (1/10)^0 (9/10)^(10-0)`
= `1 - (9/10)^10`
= `1 - (9^10)/(10^10)`
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