Question

2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is the game he is considering playing: The game costs $2 to play. He draws a card from a deck. If he gets a number card (2-10), he wins nothing. For any face card ( jack, queen or king), he wins $3. For any ace, he wins $5, and he wins an extra $20 if he draws the ace of clubs.


a) Andy's expected profit per game is: $  


b) Would you recommend this game to Andy as a good way to make money? Explain.

Yes, Andy could be lucky and might earn money in the long-run playing this game

No, we expect Andy to lose money each time he plays this game

Answer 1

Given that Andy pay &2 to play the game Probability and profits of the game can be written as below Probability of getting (2 - 10) card = 36/52 = 0.692 Therefore Profit = -2 Probability of getting face card = 12/52 = 0.231 Therefore Profit = 1 Probability of getting Any ace = 3/52 = 0.058 Therefore Profit = 3 Probability getting ace club = 1/52 = 0.019 Therefore Profit = 23 Expected profit pregame = sigma (Probability times Profit) \r\n E = (0.692) (-2) + (0.231) (1) + (0.058) (3) + (0.019) (23) = -1.384 + 0.231 + 0.174 + 0.437 E = -0.542 Since it is negative i.e. Any dy makes loss pregame Hence it is not advisable to pay It is not good way to make money