4 Recall that the Sic Bo game is played with three dice Let

4. Recall that the Sic Bo game is played with three dice. Let X denote the sum of the numbers showing after rolling three dice.
(a) Find the probability distribution of X.
(b) Suppose a player bets that the sum is 9, find the odds against this bet.
(c) Suppose the payoff of the bet in (b) is x to 1, find the largest integer x such that the house edge of the bet is positive.

Solution

(a) the probability distribution of X. = { 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}

(b) Suppose a player bets that the sum is 9, find the odds against this bet.

Favorable cases = 15

total cases = 216

bet would be = 5 : 72