Question

An assembly line has two inspectors. The probability that the first inspector will miss a defective item is 0.06. If the defective item passes the first​ inspector, the probability that the second inspector will miss it is 0.07. What is the probability that a defective item will pass by both​ inspectors?

Answer 1

probability that both passes a defective item is 0.8742‬

Explanation:

probability that the first inspector misses is Pr( 1st misses)= 0.06

therefore the probability he does not miss is

Pr(1st passes)= 1 - Pr( 1st misses) = 1 - 0.06 = 0.94

probability that the second misses is Pr( 2nd misses) = 0.07

therefore probability that 2nd does not miss is

Pr( 2nd passes) = 1- Pr( 2nd misses) = 0.93

probability that both passes a defective item is Pr(1st passes)*Pr( 2nd passes)

= 0.93*0.94 = 0.8742‬