Use Bayes' rule to find the indicated probability.
-Two shipments of components were received by a factory and stored in two separate bins.Shipment I has 2% of its contents defective,while shipment II has 5% of its contents defective.If it is equally likely an employee will go to either bin and select a component randomly,what is the probability that a defective component came from shipment II?
A)0.5
B)0.333
C)0.714
D)0.25

Question

Quizplus · Accepted Answer

Let A be the event that the defective component came from shipment I and B be the event that the defective component came from shipment II. We want to find the probability of event B given that a defective component was selected. We can use Bayes' rule to find this probability:

P(B|D) = P(D|B)P(B) / [P(D|A)P(A) + P(D|B)P(B)]

where D is the event that a defective component was selected.

We know that P(B) = P(A) = 0.5, since it is equally likely for the employee to select from either bin. Also, P(D|A) = 0.02 and P(D|B) = 0.05.

Plugging in these values, we get:

P(B|D) = 0.05(0.5) / [0.02(0.5) + 0.05(0.5)]
= 0.714

Therefore, the probability that a defective component came from shipment II is 0.714. The correct choice is C.

Use Bayes' Rule to Find the Indicated Probability