Question

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.

Answer 1

Answer:

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

                   $0.7143\ or\ 71.43\%$

Step-by-step explanation:

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:

$=\dfrac{\dfrac{1}{2}\times 0.05}{\dfrac{1}{2}\times 0.02+\dfrac{1}{2}\times 0.05}}\\\\\\=\dfrac{0.05}{0.07}\\\\=\dfrac{5}{7}\\\\=0.7143\ or\ 71.43\%$

Hence, the answer is:

                        $0.7143\ or\ 71.43\%$