A card game goes like this: You draw a card from a 52-card deck. If it is a face card (jack, queen or king), you win $6; otherwise, you lose $2. What is your expected value for this game?

Question

A card game goes like this: You draw a card from a 52-card deck. If it is a face card (jack, queen or king), you win $6; otherwise, you lose $2. What is your expected value for this game? (Round your answer to the nearest cent.)

$ 

Answer 1

First draw=12:40 for $6.

" " =40:12 for -$2.

Answer 2

P(face card) = 12/52 =3/13

P(not a face card) = 1 - 3/13 = 10/13

Expected value = (3/13)(6) + (10/13)(-2) = -2/13 = -15 cents