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

Question

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 $55. 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?

 

Can anyone

help>

Answer 1

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

 

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

 

Probability of drawing anything else:  1 - 0.013 - 0.118 = 0.869

 

0.013 * (55 - 5) = 0.647

0.118 * (25 - 5) = 2.353

0.869 * (0 - 5) = -4.347

Expected value of one play:  0.647 + 2.353 - 4.347 = -1.347.  Do not play this game.