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 $4; otherwise, you lose $2. what is your expected value for this game? (round your answer to the nearest cent.)

Answer 1

Your expected value is -$0.62.

We multiply the probability of winning by the amount won.  There are 12 face cards out of 52 cards, and the amount won is 4:

12/52(4)

We also multiply the probability of losing by the amount lost.  There are 40 cards that are not face cards out of 52, and the amount lost is 2:

40(52)(-2)

Adding these, we have: 

(12/52)(4)-(40/52)(2) = -0.62.