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.)

Question

Mathematics

Layne Hendricks

26 January, 09:43

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.)

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Jordyn Foley · 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.