Question

A certain manufactured item is visually inspected by two different inspectors. When a defective item comes through the line, the probability that the first inspector misses it is 0.1. Of those that get past the first inspector, the second inspector will "miss" 5 out of 10. What fraction of defective items get by both inspectors?

Answer 1

The fraction of a defective item getting by both inspectors is $\frac{5}{100}$ = $\frac{1}{20}$

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 = $\frac{1}{10}$.

It is given that the second inspector misses 5 out of 10 that get past the first inspector, so P(B) = $\frac{5}{10}$.

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) = $\frac{1}{10}$ × $\frac{5}{10}$ = $\frac{5}{100}$ = $\frac{1}{20}$ = 0.05%. So there is a 0.05% chance of both inspectors missing a defective part.