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The fraction of a defective item getting by both inspectors is =
Step-by-step explanation:
Step 1; Assume that the probability of the first inspector missing a defective part is P(A) and the probability of the second inspector missing those that do get past the first inspector is P(B).
Step 2; It is given that P(A) = 0.1, we convert this into a fraction so that the final probability will be a fraction and not a decimal.
P(A) = 0.1 = .
It is given that the second inspector misses 5 out of 10 that get past the first inspector, so P(B) = .
Step 3; To calculate the probability of both inspectors missing a defective part, we multiply both the probabilities.
P(A and B happening) = P(A) × P(B) = ×
=
=
= 0.05%. So there is a 0.05% chance of both inspectors missing a defective part.