Another card game. In a new card game, you start with a wellshuffed full deck and draw 3 cards without replacement. If you draw 3 hearts, you win $50. If you draw 3 black cards, you win $25. For any other draws, you win nothing.
(a) Create a probability model for the amount you win at this game, and nd the expected winnings. Also compute the standard deviation of this distribution.
My answer:
E(x)= 3.60
Standard deviation= 9.65
(b) If the game costs $5 to play, what would be the expected value and standard deviation of the net pro t (or loss)? (Hint: profit = winnings  cost; X  5)
My answer:
3.605= 1.40
(c) If the game costs $5 to play, should you play this game? Explain.
My answer:
No.. because I would lose $1.40.
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1 answer

prob(3 hearts ) = C(13,3)/C(52/3)
= 286/22100
= 11/850
expectation = (11/850)($50) = $0.647
prob(3 black) = C(26,3)/C(52,3)
= 2600/22100
= 2/17
expectation = (2/7)($25) = $2.94
expected return on the game = $3.59
You were right on the $3.60 (difference is roundoff)
agree with the loss of $1.40
again, I don't know how sd is done in this kind of problem 👍
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Reiny
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