Two different suppliers, A and B, provide a manufacturer with the same part. All

Question

Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin.

In the past, 2% of the parts supplied by supplier A have been defective,while 3% of the parts supplied by supplier B have been defective. Moreover, A supplies 4 times as many of these parts as B.

(a) What percentage of the parts are defective?

(b) Suppose you reach into the bin, select a part, and find that it is defective. What is the probability that it was supplied by B?

Youc could use tree diagrams, law of total probability or baye's formula..i'm not sure. please explain!!

Explanation / Answer

P(A) = 4/5 , P(B) = 1/5

P(D|A) = 0.02 , P(D|B) = 0.03

a)

P(D) = P(D|A)P(A) + P(D|B)P(B) = 0.02 * 4/5 + 0.03 * 1/5 = 0.022

b)

P(B|D) = P(B and D)/P(D) = P(D|B)P(B)/P(D) = 0.03 * (1/5)/0.022 = 0.2727

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