Sarah draws a card from a deck of 52 cards. She receives 40 cents for a heart, 50 cents for an ace, and 90 cents for the ace of hearts. The cost of a draw is 15 cents. How much will Sarah lose if she plays this game?

Answer 1

She wins if

1. she draws a heart, but not the ace of heart (40 cents)
Prob = 12/52
2. she draws an ace , but not the ace of heart (50 cents)
prob = 3/52
3. she draws the ace of hearts ( 90 cents)
prob = 1/52

expected return
= (12/52)(40) + (3/52)(50) + (1/52)(90)
= 13.8 cents

so if she pays 15 cents to play the game ........

Answer 2

Thanks, I could not have done this without help.