two stores sell a certain product. store a has 40% of the sales, 3% of which are of defective items, and store b has 60% of the sales, 5% of which are of defective items. the difference in defective rates is due to different levels of pre-sale checking of the product. a person receives a defective item of this product as a gift. what is the probability it came from store b?

The possibility of a possible outcome happening contingent on the frequency of a prior event or outcome is known as conditional probability.
The probability of such prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

First, we determine how likely it is that the faulty item came from store A:

P(A) = 40% x 3%

P(A) = 0.4 x 0.03

P(A) = 0.012

Next, we determine how likely it is that the faulty item came from store B:

P(B) = 60% x 5%

P(B) = 0.6 x 0.05

P(B) = 0.03

The merchandise could originate from either retailer.

Therefore, the likelihood of receiving a defective product is:

P(A) + P(B) = 0.012 + 0.03

P(A) + P(B) = 0.042

The probability defective item came from store b is;

P(defective from store b) = P(B)/ (P(A) + P(B))

P(defective from store b) = 0.03/0.042

P(defective from store b) = 0.71

P(defective from store b) = 5/7

Thus, probability defective item came from store b is 0.71.

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