In the town of Maplewood a certain type of DVD player is sold at just two stores. 36% of the sales are from store A and the rest of the sales are from store B. 7% of the DVD players sold at store A are defective while 3% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A

56.76% probability that it came from store A

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Defective.

Event B: Store A.

36% of the sales are from store A

This means that

7% of the DVD players sold at store A are defective.

This means that

Probability of a defective DVD:

36% come from store A, and of those, 7% are defective.

100 - 36 = 64% come from store B, and of those, 3% are defective. So

What is the probability that it came from store A

56.76% probability that it came from store A