一道算概率的英文題3Dice,Lotteries and LottoNote:You should write your

題目：

一道算概率的英文題3
Dice,Lotteries and Lotto
Note:You should write your answers electronically on these pages in the spaces provided.If you are working in a group,please submit only one copy.
Handwritten answers will not be accepted (except for mathematical equations if you are unable to access these with your word processor).
Question 1:
Sic bo (骰寶),also known as tai sai (大細),dai siu (大小),big and small or hi-lo,is a game of chance of ancient Chinese origin played with three dice.Grand hazard and chuck-a-luck are similar games originating in Europe.In each of these games,three (ordinary six-sided) dice are rolled and bets are made on the combinations of numbers that turn up.
(a) A bet on Any Triple wins if all three dice show the same number.What is the probability of winning on such a bet?
(b) At Star City Casino in Sydney a bet on Any Triple pays odds of 31 to 1.What is the house margin on this type of bet?A bet on a specific triple (eg 1,1,1) pays 180 to 1.Is this a better bet than Any Triple?
(c) A bet on Small wins if a total of 4 to 10 comes up,as long as the three dice don’t all show the same number,and this pays even odds.What is the probability of winning with a Small and what is the house margin for this bet?

解答：

A.P=6/(6*6*6/A3 3)
B.payoff to odds:
P=3*3*3/(6*6*6/A3 3)
E(x1)=P*31
Specific triple:
P=6/(6*6*6/A3 3)
E(x2)=p*180
Compare the values of E(x1) and E(x2),The one with higher E(x) is preferred.
C.P=1*1*1/(6*6*6/A3 3)