rahulranjan86

03-23-2012, 04:31 AM

Two shipments of machine parts are recieved. The first shipment contains 1000 parts with 10% defects and the second shipment contains 2000 parts with 5% defects. One shipment is selected at random. Two machine parts and tested and found good. Find the probability that the tested parts were selected from first shipment.

My Attempt:

Probability of selecting a shipment.

P(S) = 0.5

Probability of a part being defective when from shipment 1

P(D|1) = 0.1

Probability of a part being defective when from shipment 2

P(D|2) = 0.05

P(D) = P(D|1).P(1) + P(D|2).P(2)

P(D) = 0.075

then probability of part not being defective.

P(D') = 1 - 0.075 = 0.925

P(1|D') = P(1 and D') / P(D')

= 0.5*0.925 / 0.925

= 0.5

I have tried the above solution to the problem. I am not sure if this is correct. Please let me know if I am going wrong and how do I approach for a correct answer.

My Attempt:

Probability of selecting a shipment.

P(S) = 0.5

Probability of a part being defective when from shipment 1

P(D|1) = 0.1

Probability of a part being defective when from shipment 2

P(D|2) = 0.05

P(D) = P(D|1).P(1) + P(D|2).P(2)

P(D) = 0.075

then probability of part not being defective.

P(D') = 1 - 0.075 = 0.925

P(1|D') = P(1 and D') / P(D')

= 0.5*0.925 / 0.925

= 0.5

I have tried the above solution to the problem. I am not sure if this is correct. Please let me know if I am going wrong and how do I approach for a correct answer.