A manufacturing company has a 2% defect rate. If 7 items are chosen at random, what is the probability that one will have a defect?

Answer 1

Recall the binomial probability formula P(X=x) = C(n,x)p^xq^n-x where q=1-p and C(n,x) = n!/[x!(n-x)!]

P(X=1) = C(7,1)(0.02)¹(0.98)⁶ ≈ 0.124

Therefore, the probability of selecting one with a defect is about 0.124

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