3.31 Hearts Win

Philip Tanofsky

DATA 606

September 18, 2019

Problem Statement

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.

P(3 hearts) = P(13/52) x P(12/51) x P(11/50) = 0.0129

P(3 black cards) = P(26/52) x P(25/51) x P(24/50) = 0.1176

Part 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.

A: E(X) = \$3.59. SD(X) = 9.64.

Part 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 âˆ’ cost;
X âˆ’ 5)

Answer: E(X) = -\$1.41. SD(X) = 9.64.

Part C

If the game costs \$5 to play, should you play this game? Explain.

Answer: No, the expected net profit is negative as calculated in part B (loss of \$1.41), so on average one would expect to lose money if the game costs \$5.

Thank you.