2011-5-17 23:59
siun0528
統計數學問題,賭場買大小,急急
Small: wins on total of 4-10, except for a three of a kind. Pays 1 to 1.
Big: wins on total of 11-17, except for a three of a kind. Pays 1 to 1.
4: wins of total of 4. Pays 50 to 1.
5: wins on total of 5. Pays 18 to 1.
6: wins on total of 6. Pays 14 to 1.
7: wins on total of 7. Pays 12 to 1.
8: wins on total of 8. Pays 8 to 1.
9: wins on total of 9. Pays 6 to 1.
10: wins on total of 10. Pays 6 to 1.
11: wins on total of 11. Pays 6 to 1.
12: wins on total of 12. Pays 6 to 1.
13: wins on total of 13. Pays 8 to 1.
14: wins on total of 14. Pays 12 to 1.
15: wins on total of 15. Pays 14 to 1.
16: wins on total of 16. Pays 18 to 1.
17:wins on total of 17. Pays 50 to 1.
Triple : wins if all 3 dice match the number chosen. Pays 150 to 1.
Any triple: wins on any three of a kind. Pays 24 to 1.
Questions:
1. Use classical approach to calculate the probabilities of all events (i.e. betting possibilities) defined above. Explain briefly why the sum of these probabilities is greater than 1. (老師話order係唔重要,不用跟order)
2. Suppose you are considering placing a bet of $2,000 on any one of the events. Calculate and rank the long=run expected returns of each strategy. (用expected value 計算)
3. Suppose you are considering placing a bet of $2,000 on any one of the events. Calculate and rank the riskiness of each strategy. What can you conclude from your calculations from 2 and 3?
4. Suppose a gambler is offered the following betting possibility:
ODD: wins if odd number. Pays 1.1 to 1.
As far as the casino offering this betting probability is concerned, what is wrong with this offer?
5. Suppose you are planning to open a new casino and assume all other costs are zero, except the payoff amounts. To be competitive (im terms of odds), what are the maximum and minimum odds of “10”?
全部questions要有步驟!