In a new card game, you start with a well-shuffled 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 find the expected winnings. Also compute the standard deviation of this distribution. (b) If the game costs $5 to play, what would be the expected value and standard deviation of the net profit (or loss) ? (Hint: profit = winnings - cost; X - 5) (c) If the game costs $5 to play, should you play this game? Explain.

Question

Mathematics

Spanky

14 March, 18:50

In a new card game, you start with a well-shuffled 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 find the expected winnings. Also compute the standard deviation of this distribution. (b) If the game costs $5 to play, what would be the expected value and standard deviation of the net profit (or loss) ? (Hint: profit = winnings - cost; X - 5) (c) If the game costs $5 to play, should you play this game? Explain.

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Answers (1)

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Jakob Fuentes · Answer 1

Expected pay winning $50 = $0.585

Expected pay winning $25 = $2.36

Expected pay for anything else = $-4.35

Expected returns=3.59

Expected value for one play = $ (-1.41)

Do not play this game because you will lose $1.41

Step-by-step explanation:

Probability P (3 hearts) = (13/52) * (12/51) * (11/50) = 0.013

Probability P (3black) = (26/52) * (24/51) * (23/50) = 0.118

Probability P (drawing anything else) = 1 - 0.013 - 0.118 = 0.869

Expected pay ($50) = 0.013$ (50-5) = $ 0.585

Expected pay ($25) = 0.118 (25-5) $ = $2.36

Expected pay for anything else = 0.869 (0-5) $ = $ (-4.347)

Expected value of one play=$ (0.585 + 2.353 - 4.347) = - $1.41

c) Do not play the game.