Question

A company produces widgets in three factories, A, B and C. Factory A produces 20% of the widgets, factory B produces 45% of the widgets and factory C produces the remaining 35%. Of all widgets produced, 5% fail tolerance. Of those that fail tolerance, 25% were produced in factory A, 35% were produced in factory B and 40% were produced in factory C.

In factory A, what percentage of the widgets produced fails tolerance?

Answer 1

1.25% widgets from factory A fail.

Explanation:

Probability of widgets that fail = 0.05

Probability of failing widget to belong from factory A = 0.25

Probability of failing widget to belong from factory B = 0.35

Probability of failing widget to belong from factory C = 0.40

Probability of factory A widgets failing = Probability of widgets failing * probability they belonged from factory A

Probability of factory A widgets failing = 0.05 * 0.25 = 0.0125

This probability stated as percentage: 1.25%