Question

You are playing a game where you draw a card from a standard deck, and you will win $5 if you draw a face

card, $14 if you draw an ace and lose $19 if you draw any other card. What is the expected gain from this
game?

Answer 1

Since there are 12 face cards (4 J, 4 Q, 4K) those represent 12/52. The nonface cards excluding aces (4 twos through 4 tens) represent 36/52.

The expected value is then:

(12/52)($3)+(36/52)(-$2)= -$36/52 or -$0.69 but rounding to one decimal would be -$0.70