Consider a keno game in which the casino draws 10 balls out of 40. A bet is available on a pick 6.

1. How many ways can the player catch 3 out of 6? (4 points)

 

 

 

 

 

 

2. How many ways can the player catch 4 out of 6? (4 points)

 

 

 

 

 

 

 

3. How many ways can the player catch 5 out of 6? (4 points)

 

 

 

 

 

 

4. How many ways can the player catch 6 out of 6? (4 points)

5. What is the total number of combinations for picking 6 numbers out of 40? (4 points)

6. Following is the pay table. Fill in the rest of the table to find the expected return. (4 points)

Expected return = ______________________ (4 points)

7 At an Internet casino you see the following bets available on who will win the 2008 presidential election. Assume the expected return is the same on all bets, what is it? (10 points)

8. You question the fairness of a video poker game on the deal. So you test 649,740 hands. The following table shows your expected and actual results. Fill in the last row to find the chi-squared statistic. (10 points)

What is the chi-squared statistic?____________________

9.

What is the p value? _________ (5 points)

For problems 11 to 16 consider a blackjack side bet based on the player’s first two cards and the dealer’s up card. There are five decks in the shoe.

10. How many ways can the player get 3 suited fives? (4 points)

11. How many ways can the player get a suited 4, 5, 6 (one of each)? (4 points)

 

 

 

 

 

 

 

 

12. How many ways can the player get a non-suited 555? (4 points)

 

 

 

 

 

 

 

 

13. How many ways can the player get a non-suited 4, 5, 6 (one of each)? (4 points)

 

 

 

 

 

 

 

14. How many ways can the player get a flush (not including suited 555 and 456)? (4 points)

 

 

 

 

 

 

 

15. Fill in the following table to find the expected return. (4 points)

Hand	Pays	Probability Combinations	Return Combinations
Suited 555	5000 to 1
Suited 456	500 to 1
Non-suited 555	200 to 1
Non-suited 456	100 to 1
Flush	5 to 1
All other	Loss
Total	.

Expected return = ________________________

 

 

16. At the Cal-Neva in Reno a bet on a player blackjack pays 17 to 1. What is the house edge in a 2-deck game? (7 points)

 

 

 

 

 

 

 

 

 

 

17. Your sock drawer has 7 blue socks, 5 green socks, and 3 red socks. You pick 5 socks at random and without replacement. What is the probability you pick 3 blue socks and 2 green socks? (7 points)

 

 

 

 

 

 

 

 

 

 

18. In the game of Clue^® there are 9 room cards, 6 weapon cards, and 6 suspect cards. You shuffle them and draw 3 at random. What is the probability you draw one of each? (7 points)