Question

Can someone give me an example of using permutation probability for the game backgammon.

Answer 1

The probability of rolling two dice and getting at least one of a number from 1 to 6 is straightforward to calculate. If we wish to determine the probability of rolling at least one 2 with two dice, we need to know how many of the 36 possible outcomes include at least one 2. The ways of doing this are:

(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6)

Thus there are 11 ways to roll at least one 2 with two dice, and the probability of rolling at least one 2 with two dice is 11/36.