Use Bayes' theorem to find the indicated probability.
-In the town of Maplewood a certain type of DVD player is sold at just two stores. 45% of the sales are from store A and 55% of the sales are from store B. 2.5% of the DVD players sold at store A are defective while 4.7% 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?
A) 0.697
B) 0.303
C) 0.025
D) 0.435

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the probability that the defective DVD player came from store A is calculated as follows: P(A|D) = [P(D|A) * P(A)] / [P(D|A) * P(A) + P(D|B) * P(B)] = [0.025 * 0.45] / [0.025 * 0.45 + 0.047 * 0.55] = 0.303.

Use Bayes' Theorem to Find the Indicated Probability