Question

We have the choice between 2 games.  Both require a $5 bet.  Make a decision as to which game you would play based on the probability distributions below.  Let X represent amount of money won/lost.  You can either lose your $5, get your $5 back (break even), win double ($10), triple ($15) or quadruple ($20) your money.

1. If you win $10, what is your profit?

2. If you win $15, what is your profit?

3. If you win $20, what is your profit?

The following tables contain the discrete probability distributions of profit for the two games. Use these tables to answer questions 11- 20:

GAME 1:

X	-5	0	5	10	15
P(x)	0.263	0.369	0.264	0.088	0.016

GAME 2:

X	-5	0	5	10	15
P(x)	0.2	0.2		0.2	0.2

4. Is the distribution for Game 1 a valid probability distribution? Yes/No, and why.

5. What is the probability you lose or break even in Game 1? Include your probability statement.

6. What is the probability of leaving with a profit in Game 1?

7. What is the probability of winning a $5 profit (they give you $10) in Game 1?

8. Find the mean amount of money won for Game 1. (Expected Value)

9. Find the standard deviation of money won for Game 1.

10. Use the range rule of thumb to identify the range of values for usual amount of money won/lost for Game 1.

The maximum usual value is:

The minimum usual value is:

11. Is the chance of winning a profit of $10 or more in Game 1 significant?

12. Complete the table for Game 2 making it a valid probability distribution.

13. Find the Expected value for money won in Game 2. (Expected Value)

14. Find the standard deviation of money won for Game 2.

15. Which game would you play, and why?

16. If you were the casino boss, would you be happy with either game?

Answer 1