For this problem, assume that the outcomes 1 through 3 are equally likely, that the outcomes 4 through 6 are equally likely, and that the outcome 1 is three times as likely as outcome 4.

Question

1) What probability should be assigned to rolling a 1?

2) What probability should be assigned to rolling a 4?

Answer 1

This problem is best solved with a little algebra. Since outcome 1 is three times as likely as outcome 4, let the probability of outcome 4 equal x, so that the probability of outcome 1 is 3x.

Since the sum of the probabilities of all outcomes must be 1 (a truism about probability distributions), the sum of the probabilities of outcome 1, outcome 2, ... and outcome 6 equals 1. So:

3x + 3x + 3x + x + x + x = 1

12x = 1

x = 1/12 (which is the probability of outcome 4).

and 3x = 3(1/12) = 3/12 = 1/4 is the probability of outcome 1.