Question

g Two different factories named A and B both produce an automobile part. If a part came from A, the probability that the part is defective is .04. If the part came from B, the probability that it is defective is .05. In a sample of 180 parts, 100 came from A and 80 came from B. (a) What is the probability that a part chosen at random (from the sample) was defective

Answer 1

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

Explanation:

Probability of a defective part:

0.04 of
`(100)/(180)`, that is, coming from A.

0.05 of
`(80)/(180)`, that is, coming from B. So

`p = 0.04(100)/(180) + 0.05(80)/(180) = (0.04*100 + 0.05*80)/(180) = 0.0444`

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.