A card game goes like this: You draw a card from a 52-card deck.

Question

If it is a face card (jack, queen or king), you win $3; otherwise, you lose $2. Suppose that this game is modified so that if you draw an ace, then no money changes hands. What is your expected value for this game? (Round your answer to one decimal place.)

Incorrect: Your answer is incorrect.
28.6%  I don't understand why my answer is wrong. The ace shouldn't matter. It's face cards. 

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

Answer 2

For the face cards:  3(4/52)

For the non-face: -2(36/52)  the Ace was excluded

 

3(4/52) - 2(36/52)

 

-15/14

-1.071