GAM 470 Test #1

February 22, 2005

Name______________________________

All problems are worth 4 points each, except the last two, which are 6 points each.

Problems 1 to 6: An octahedron is an 8-sided die. Imagine a craps game in which two octahedrons are rolled.
  1. What is the probability the two dice have a total of 3?

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  2. If a total of 3 pays 25 to 1 what is the expected value?

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  3. A place bet may be made that a total of 12 is rolled before a total of 9. What is the probability of winning?

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  4. The place bet on a 12 before a 9 pays 3 to 2. What is the house edge?

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  5. The player may bet on over or under a total of 9. What is the probability the total is under 9?

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  6. The under 9 bet pays 1 to 1. What is the expected value?

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    Problems 7-12: Consider a Sic Bo game with four six-sided dice.

  7. The player may bet on a four of a kind. The bet wins if all four dice are the same face. What is the probability of winning?

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  8. The four of a kind bet pays 200 to 1. What is the house edge?

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  9. The player may also bet on a two pair. The bet wins if two different numbers appear, each twice. For example {3,3,5,5}. What is the probability of winning?

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  10. The two pair bet pays 12 to 1. What is the expected value?

 

 

 

 

 

 

Consider a bet in which the player picks any number from 1 to 6. The player is paid according to the number of times his number appears according to the following table.

Appearances

Pays

0

Loss

1

Push

2

2 to 1

3

10 to 1

4

50 to 1

11. What is the probability of winning per roll?

 

 

 

 

 

 

 

12 What the house edge of the bet in problem 11?

 

 

 

 

 

 

 

 

Problems 13-15: Consider a drawer with 6 red socks, 4 green socks, and 2 yellow socks.

13. You pull out three socks at random without replacement. What is the probability you pick one of each color?

 

 

 

 

 

 

14. You pull out four socks at random without replacement. What is the probability you get a two pair, in other words two different colors of two socks each?

 

 

 

 

 

 

 

15 You pull out six socks at random and without replacement. What is the probability you pull out exactly three reds?

 

 

 

 

 

 

 

Problems 16-17: Another sock drawer has 5 blue socks, 5 orange socks, and 5 purple socks.

16 You pull out three socks at random and without replacement. What is the probability you have at least 2 of the same color?

 

 

 

 

 

 

 

 

 

17 You pull out five socks at random and without replacement. What is the probability you get a full house (3 of one color and 2 of another)?

 

 

 

 

 

 

 

 

 

Problems 18-22: You have a deck of cards consisting of 13 ranks of 5 suits each. Dealing five cards at random and without replacement what is the probability of the following hands?

18 A full house

 

 

 

 

 

 

19 A straight (aces count high or low). Straight does not include straight flush.

 

 

 

 

 

 

20 A three of a kind

 

 

 

 

 

 

21 A flush. Flush does not include straight flush.

 

 

 

 

 

 

 

22 A two pair

 

 

 

 

 

 

 

Problems 23-23: The slot machine Test Anxiety has the following pay table.

Payline

Pays

3 clocks

500

3 coffee cups

100

3 books

50

3 pencils

40

3 notes

30

3 chairs

20

3 calculators

5

Any 2 clocks

5

Any 1 clock

2

Following is how each symbol is weighted on each reel.

Symbol

Reel 1

Reel 2

Reel 3

coffee cup

2

1

1

book

2

2

1

pencil

2

2

2

notes

3

2

2

chair

4

4

4

calculator

4

6

7

clock

1

1

1

total

18

18

18

Fill in the table below to determine the hit frequency and the expected return.

Payline

Pays

Probability Combinations

Return Combinations

3 clocks

500

3 coffee cups

100

3 books

50

3 pencils

40

3 notes

30

3 chairs

20

3 calculators

5

Any 2 clocks

5

Any 1 clock

2

Total

 

23. What is the hit frequency? (6 points)

 

 

24. What is the expected return? (6 points)