if you draw a card value of 4 or less from a standard deck of cards, i will pay you $18. if not you pay me $9. find the expected value proposition

Answer 1

Cards less than or equal to 4: ace, 2, 3 and 4. 4 suits, so 16 cards out of 52 are less than or equal to 4, so probability of drawing less than or equal to 4 is 16/52 = 4/13

Event Amount P(Amount)

Card 4 or less 18 4/13

Card 4 or greater -9 9/13

Expected Value = 18 * 4/13 - 9 * 9/13 = -9/13 = $-0.69