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. 43% of the sales are from store A and 57% of the sales are from store B. 2.4% of the DVD players sold at store A are defective while 4.0% 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) 0.453
B) 0.024
C) 0.312
D) 0.688

Question

Quizplus · Accepted Answer

Let's use Bayes' theorem:
P(A|D) = (P(D|A) * P(A)) / P(D)
We want to find P(A|D), the probability that the DVD player came from store A given that it is defective. 
P(D|A) = 0.024, the probability that a DVD player from store A is defective. 
P(A) = 0.43, the probability that a DVD player was purchased at store A. 
P(D) = (P(D|A) * P(A)) + (P(D|B) * P(B)) = (0.024 * 0.43) + (0.04 * 0.57) = 0.03108, the probability that any DVD player is defective. 
Now we can plug in the values: 
P(A|D) = (0.024 * 0.43) / 0.03108 = 0.312.

Therefore, the answer is C) 0.312.

Use Bayes' Theorem to Find the Indicated Probability