Question

A product test is designed in such a way that for a defective product to be undiscovered, all four inspections would have to fail to catch the defect. The probability of catching the defect in inspection 1 is 90%; in inspection 2, 80%; in inspection 3, 12%; and in inspection 4, 95%. What is the probability of catching a defect?a. 0.008% b. 62.9% c. 37.7% d. 99.9%

Answer 1

d. 99.9%

Explanation:

The probability of not catching a defect for each inspection is 100% minus the probability of catching a defect. The probability that a defect is not caught in all four inspections is the product of each inspection's individual probability:

`P(D) = (1-0.9)*(1-0.8)*(1-0.12)*(1-0.95)\\P(D) = 0.0008`

The probability of catching a defect is given by:

`P(C) =  1 - P(D)\\P(C) = 1 - 0.0008\\P(C) = 0.9992 = 99.9\%`

There is a 99.9% probability of catching a defect.