In a game of craps two dice are rolled and the up faces are

In a game of craps two dice are rolled and the up faces are totaled. If the person rolling the dice on the first roll rolls a 7 or an 11 they win. If they roll a 2,3,or 12 on the first roll they lose. If they roll any other total then on subsequent rolls they must roll that total before rolling a 7 to win. What is the probability of winning on the first roll?

Solution

To win on the first roll, you have to get a 7 or 11. These are the possibilities:

1   6
2   5
3   4
4   3
5   2
6   1
5   6
6   5

So, there are 8 ways to win on first roll. There are 6*6 = 36 ways to roll.

Thus,

P(win on first roll) = 8/36 or 0.222222222 [ANSWER]