Question

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.If the game costs $5 to play, what is the expected value?

Answer 1

Answer: −1.409

Step-by-step explanation:

Probability of drawing 3 hearts: 13/52 * 12/51 * 11/50 = 0.013

Probability of drawing 3 black cards: 26/52 * 25/51 * 24/50 = 0.118

Probability of other draw: 1 - 0.013 - 0.118 = 0.869

0.013 * (50 - 5) = 0.585

0.118 * (25 - 5) = 2.353

0.869 * (0 - 5) = -4.347

Expected value: 0.585+ 2.353 - 4.347 = -1.409