1. Suppose there are two full bowls of cookies.

Bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each.
Our friend Fred picks a bowl at random, and then picks a cookie at random.
We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies.
The cookie turns out to be a plain one.
How probable is it that Fred picked it out of Bowl #1?

3 answers

To get a plain cookie:

we could have (1,P) or (2,P)
prob (1, P)= (1/2)((30/40) = 3/8
prob (2,P) = (1/2)(20/40) = 1/4

prob(plain cookie) = 3/8 + 1/4 = 5/8

(checking:
prob(1,C) = (1/2)(10/40) = 1/8
prob(2,C) = (1/2)(20/40) = 1/4
note 3/8+1/4+1/8+1/= 1 , check! )

could have stopped at
prob (1, P)= (1/2)((30/40) = 3/8

p1 p2 3/8

3/8 cookies