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. it is equally likely an employee will go to either bin and select a component randomly. use bayes' rule to find the probability that a defective component came from shipment ii.

The probability that a defective component came from shipment II is:

Let A denote the event that the defective component was from shipment I

Also, P(A)=2%=0.02

and B denote the event that the defective component was from shipment II.

i.e. P(B)=5%=0.05

Also, P(shipment I is chosen)=1/2=0.5

and P(shipment II is chosen)=1/2=0.5

The  probability that a defective component came from shipment II is calculated by Baye's rule as follows:

Hence, the answer is:

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.