Another card game. In a new card game, you start with a well-shuffed 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.

Question

(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:
3.60-5= -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.

Answer 1

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