Question

Suppose 1% of cotton fabric rolls and 4% of nylon fabric rolls contain flaws. Of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. What is the probability that a randomly selected roll used by the manufacturer contains flaws?

Answer 1

0.019 or 1.9%

Explanation:

The probability that a randomly selected roll used by the manufacturer contains flaws is determined by the probability of a flawed cotton roll occurring (1% x 70%) added to the probability of a flawed nylon roll occurring (4% x 30%) .

`P(F) = P(C)*P(F_C)+P(N)*P(F_N)\\P(F) = 0.7*0.01+0.3*0.04\\P(F) = 0.019 = 1.9\%`

The probability that a randomly selected roll contains flaws is 0.019 or 1.9%