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.

Answer 1

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) = ⁿC_xp^xq^n−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)`