You are challenged to a lucky draw game. if you draw a face card (k, q, j) from a standard deck of cards, you earn 10 points. if you draw any other card, you lose 2 points. what is the expected value of a draw? a. 0.77 b. 1.69 c. 1.85 d. 2.31

The deck has 52 cards. 

... There are 4 kings, 4 queens, and 4 jacks.
    So the probability of earning 10 points is  (12/52) = 23.1% .

... There are 40 other cards.
    So the probability of losing 2 points is   (40/52) = the other 76.9% .

The expected value of the draw is

             (0.231 x 10)  -  (0.769 x 2)  

          =      (2.31)      -      (1.538)

          =    win  +0.769 of a point . 

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