HMD 436 Name___________________

Final Exam

May 13, 2002 6:00-800 PM

 

  1. What is the probability of rolling a total of 2 with two ordinary dice? (2 points)

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  2. What is the probability of rolling a total of 6 with two ordinary dice? (3 points)

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  3. Two cards are drawn from an ordinary deck without replacement. What is the probability they are both the same rank? (3 points)

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  4. What is the probability of drawing a blackjack from a 4-deck shoe? (3 points)

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  5. You have seven rooms in your house. Every day you clean each room. To avoid boredom you clean then in a different order every day. How many days can you go before repeating an order? (3 points)

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  6. At your favorite Las Vegas arcade there are 12 video games. Each day you play a different combination of four of them. How many days can you go without playing the same combination twice? (3 points)

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  7. An urn contains 10 black balls and 15 white balls. You draw 6 balls at random without replacement. What is the probability you draw 2 black balls and 4 white balls? (3 points)

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  8. Two ordinary dice are rolled until a total of 5 is obtained. What is the expected number of rolls this will take? (3 points)

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  9. How many different combinations of 7 cards can be dealt from a single deck of cards? (3 points)

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  10. What is the probability of drawing a full house from a single deck of ordinary cards? (3 points)

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  11. The shooter in craps must roll a total of 9 before rolling a 7. He keeps rolling until either total is obtained. What is the probability of rolling the 9 first? (3 points)

 

 

 

 

 

 

12. What is the probability of being dealt (before the draw) a sequential royal flush in either direction in normal 52-card deck video poker? (4 points)

 

 

 

 

 

 

 

For questions 13,14 consider a modified deck with 16 ranks and 6 suits. The ace can be high or low.

  1. How many combinations are there for a flush (not including straight flush)? (5 points)

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  2. How many combinations are there for a two pair? (5 points)

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    Problems 15,16 are all based on blackjack side bets.

  3. In an eight-deck shoe what is the probability of drawing four aces of the same color in the first four cards? (5 points)

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  4. In a six-deck shoe what is the probability of drawing two non-suited sevens as the first two cards, and then a non-7 as the third card? (5 points)

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  5. In bingo what is the probability the player will form a frame shape (covering all the edges of the card) within 50 calls? (6 points)

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  6. What is the probability in a room of 500 cards at least one player will form a frame shape within 50 calls? (4 points)

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  7. Consider the following money line.

    8. Chicago (-140) Vs. Houston (+120).

    Assuming a fair set of lines would have been -130 and +130 what is the probability that Atlanta will win? (4 points)

     

     

     

     

     

     

     

     

     

  8. From the above problem what is the expected value for a bet on Chicago? (4 points)

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  9. Assume the player has a 70% chance of correctly picking a football game with a free 7 points. A 5-team 7-point teaser pays 7-2. What is the expected value? Ignore ties. (5 points)

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  10. The total amount bet on place bets at Prairie Meadows is $100,000. The track cut on place bets is 18%. The two placing horses are 4 and 7. $6000 is bet on 4 and $9000 on 9. How much is a $20 place bet on horse 4 worth (including the original $20 which is refunded)? The track has a 10-cent breakage. (5 points)

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  11. A double-zero roulette player bets $1 on a 4-number combination bet (which pays 8-1) 500 times. Using the normal distribution is what is the probability that the player wins $100 or more? Also indicate the Z statistic. (8 points)

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  12. A casino uses a promotional prize wheel. The wheel should stop on each prize with the following probabilities:

    13. Key chain 30%

    Deck of cards 20%

    Buffet coupon 15%

    Show ticket 10%

    Dice clock 10%

    T-shirt 10%

    Jacket 4%

    $1000 1%

    Following is the wheel’s actual and expected results over 10,000 spins. You may use the chi-squared column for your own work. What is the chi-squared statistic and what is the probability that a fair test would be this skewed or more? (8 points)

    Prize

    Expected

    Actual

    Chi-squared

    Key chain

    3000

    2970

    Deck of cards

    2000

    1920

    Buffet

    1500

    1440

    Show ticket

    1000

    1020

    Dice clock

    1000

    1040

    T-shirt

    1000

    1060

    Jacket

    400

    430

    $1,000

    100

    120

    Total

    10000

    10000

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

  13. Briefly explain how Japanese pachinko parlors get around the law prohibiting the exchange of balls back into cash? (4 bonus points)