Question

Items are inspected for flaws by two quality inspectors. If a flaw is present, it will be detected by the first inspector with probability 0.9, and by the second inspector with probability 0.7. Assume the inspectors function independently.

a. If an item has a flaw, what is the probability that it will be found by both inspectors?
b. If an item has a flaw, what is the probability that it will be found by at least one of the two inspectors?

Answer 1

Answer:0.63

0.97

Explanation:

Given

Probability to detect the flaw by first inspector is 0.9

Probability to detect the flaw by second inspector is 0.7

(a)Probability that both inspector find the flaw

`P=0.9* 0.7=0.63`

(b)Probability of finding flaw by at least one inspector is

P=1-Probability of not detecting the flaw by both inspectors

`P=1-\left ( 1-0.9\right )\left ( 1-0.7\right )`

P=1-0.03=0.97