Discrete Math Q4].. . [10 points] Two different factories named A and B both pro

Question

Discrete Math

Q4].. . [10 points] Two different factories named A and B both produce an automobile part. If a part came from A, the probability that the part is defective is 02 If the part came from B, the probability that it is defective is .05. In a sample of 180 parts, 100 came from A and 80 came from B a) What is the probability that a part chosen at randon (from the sample) came from A? (b) Suppose that we have found a defective part in the sample. Find the probability that this part came from A

Explanation / Answer

a) Given n(S)=180,n(A)=100

Probability that a part came from A is = n(A)/n(S)

=100/180

=0.55

b) given in the data that

Probability of that the part came from A is defective=P(D/A)=0.02

Probability of that the part came from B is defective=P(D/B)=0.05

Using Bayes theorem,

Probabiity that the defective came from A is P(A/D)=[P(D/A)P(A)]/[P(D/A)P(A)+P(D/B)P(B)]

=0.282

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