PROBLEM 14E

Two processes of a company produce rolls of materials: The rolls of Process I are 3% defective and the rolls of Process II are 1% defective. Process I produces 60% of the company’s output, Process II 40%. A roll is selected at random from the total output. Given that this roll is defective, what is the conditional probability that it is from Process I?

Step 1 of 2:

Given that, a company has two processes to produce raw materials, namely process I and process II.

3% of rolls of process i are defective,that is P(defective rolls| they are from process I)=0.03.

1% of rolls of process II are defective, that is P(defective rolls given they are from process II)=0.01.

Process I produces 60% of company’s output.Therefore P(process I)=0.6.

Process Ii produces 40% of company’s output.Therefore P(process II)=0.4.

A roll is selected randomly. We have to find the conditional probability of process I given that the selected roll is defective.