SOLUTION: Mary bakes 8 chocolate chip cookies and 10 peanut butter cookies. Bill bakes 5 chocolate chip cookies and 10 peanut butter cookies. The 33 cookies are put together and offered on a

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Question 1165446: Mary bakes 8 chocolate chip cookies and 10 peanut butter cookies. Bill bakes 5 chocolate chip cookies and 10 peanut butter cookies. The 33 cookies are put together and offered on a single plate. I pick a cookie at random from the plate.
(a) What is the probability that the cookie is chocolate chip?

(b) What is the probability that Mary baked the cookie?

(c) What is the probability that the cookie is chocolate chip given that Mary baked it?

(d) Use Bayes's theorem to calculate the probability that the cookie is baked by Mary given that it is chocolate chip. In this situation, Bayes's theorem tells us that
P(Mary given Chocolate) = P(Chocolate given Mary) × P(Mary)
P(Chocolate)

(e) Calculate without using Bayes's theorem the probability that the cookie is baked by Mary given that it is chocolate chip. Suggestion: How many of the chocolate chip cookies were baked by Mary?

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
13 C
20 PB
a. 13/33 probability
b. 18/33 or 6/11
c. 8/18 or 4/9
d. P(M|C)=8/13
=P(C|M)=4/9
P(M)=6/11
P(C)=13/33
4/9*6/11 divided by 13/33
that is (24/99)divided by 13/33
or 8/33 divided by 13/33
which is 8/13, which is what was described above and is what is wanted for e.