Question

There are 2 wallets. The first wallet has 2 twenty dollar bills and 3 five dollar bills. The second wallet has 1 fifty dollar bill, 1 twenty dollar bills, and 2 five dollar bills. One wallet is selected randomly.

What is the probability the first two bills selected sum to at least $40.

If you know the first bill is a 20 dollar bill, what is the probability it is from the first wallet? (If it's important to you, I can make another question so you get two medals)

Answer 1

P(at least $40 | first wallet) = 2/5 . 1/4 , because we need to select the two $20 bills
= 1/10
P(at least $40 | second wallet) = 2/4 . 1/3 , because we need to select the $50 and $20 bill
= 1/6

Hence

P(at least $40) = P(at least $40 | first wallet) P( first wallet )
+ P(at least $40 | second wallet) P( second wallet )
= 1/10 . 1/2 + 1/6 . 1/2
= 2/15

Answer 2

then for the second question, use Bayes Theorem:

P(1st wallet | $20 bill) = P($20 | 1st) P(1st) / P($20)
= 2/5 . 1/2 / (something you can figure out)