If you draw a card with a value of three or less from a stan

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $6. If not, you pay me $5. (Aces are considered the highest card in the deck.) Find the expected value of the proposition

Solution

Expected Value = P(Gain)*Value(Win) - P(Loss)*Value(Loss)

Value(Gain) = 6
Value(Loss) = -5

P(Gain) = P(three or less) = 8/52 = 0.1538
P(Loss) = 1 - P(Win) = 1 - .0.1538= 0.8462

EV = (6)*(0.1538) + (-5)*(0.8462) = -$3.3082 Answer