Use Bayes's 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)0.333
B)0.25
C)0.5
D)0.714

Question

Use Bayes's 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)0.333
B)0.25
C)0.5
D)0.714

Quizplus · Accepted Answer

Bayes's rule formula for this problem is P(II|Defective) = [P(Defective|II) * P(II)] / P(Defective). Given that P(Defective|I) = 0.02, P(Defective|II) = 0.05, and both shipments are equally likely, so P(I) = P(II) = 0.5. The overall probability of getting a defective component, P(Defective), is the sum of the probabilities of getting a defective component from each shipment, weighted by the probability of choosing that shipment: P(Defective) = P(Defective|I) * P(I) + P(Defective|II) * P(II) = 0.02 * 0.5 + 0.05 * 0.5 = 0.035. Therefore, P(II|Defective) = (0.05 * 0.5) / 0.035 = 0.714.

Use Bayes's Rule to Find the Indicated Probability