Hearts win. In a new card game, you start with a well- shued full deck and draw

Question

Hearts win. In a new card game, you start with a well- shued 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. Hearts win. In a new card game, you start with a well- shued 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. Hearts win. In a new card game, you start with a well- shued 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.

Explanation / Answer

(a)Let X represents winning amount

then P(X=50)=P(3 hearts) = 4C3/52C3 = 0.00018099547

P(X = 25) = P(3 black cards) = 26C3/52C3 =0.11764705882

P(X=0) = 1- 0.00018099547 - 0.11764705882 = 0.88217194571

Expected winnings E(X)= 50*0.00018099547+ 25*0.11764705882 = 2.950226244

Standard deviation = E(X^2)-E(X)^2

=2500*0.00018099547 +625*0.11764705882 - 2.950226244^2 =65.2780655467

(b)net profit= expected profit - loss = 2.950226244 - 5 =-2.049773756, it is a loss of 2.049773756

(c)No, since it is a loss

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