Question

Bart's Bakery makes two kinds of pies: apple and blueberry. If you select a pie at random, the probability it is apple is 0.88. Bart's Bakery also makes two sizes of pies: large and small. The probability a randomly selected apple pie is large is 0.60. The probability a randomly selected blueberry pie is large is 0.75. Given that a randomly selected pie is small, what is the probability it is an apple pie?

Group of answer choices

0.9215

0.0785

0.1456

0.8544

Answer 1

Solution:

Let

A = Apple pie

B = Blueberry pie

P(A) =0.88

P(B) =1-P(A) = 1 - 0.88 = 0.12

Let S = Small and L = Large

P(L|A) = 0.60

then

P(S|A) = 1 - P(L|A)

P(S|A) = 1 - 0.60

P(S|A) = 0.40

and

P(L|B) =0.75

then

P(S|B) = 1 - P(L|B)

P(S|B) = 1 -0.75

P(S|B) = 0.25

We have to find:

P( an apple pie | pie is small) =...............?

P(A | S) =...........?

Using Bayes rule: