Exercise 31

Hearts win. 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.

1. 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.

2. 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; $X-5$)

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