Expected value in cents

Question

You have 4 quarters and 3 dimes in your pocket. You draw two out at random. What is the expected value of the coins in cents that you draw?

Answer 1

total expected value = expected value of 2 quarters

+ expected value of 2 dimes

+ expected value of 1 dime and 1 quarter

Prob(quarter) = 4/10 = 2/5

Prob(dime) = 3/10

Prob( 2 quarters) = 4/10 * 3/9 = 2/5*1/3 = 2/15

Prob( 2 dimes) = 3/10 * 2/9 = 6/90 = 1/15

Prob(1 dime and 1 quarter) = 4/10 * 3/9 + 3/10*4/9 =

12/90 + 12/90 = 24/90 = 12/45 = 4/15

Amount in pennies:

50*2/15 + 20*1/15 + 35 * 4/15 =

(100 +20 + 140)/15 = 260/15 = 17.33