HELP WITH FINITE ASAP

Question

In a game that costs $2 to play, a player selects a card at random from a standard deck. The player earns $12 for selecting an ace, $3 for selecting a face card, and nothing for selecting any other card. Find the expected value of net gain OR loss.

Answer 1

Prob(ACE) = 4/52 = 1/13

Prob(FACE) = 12/52 = 6/26= 3/13

Prob(other) = 36/52 = 18/26 = 9/13

(12-2)*1/13 + (3-2)*3/13 + (0-2)*9/13 =

10/13 + 1/13 -18/13 =

-7/13 =

-0.53846153846153846153846153846154