We are given that a die is weighted in such a way that each of 1 and 2 is three times as likely to come up as 3, 4, 5, or 6. We are asked to find the probability distribution associated with this die. The probability of each outcome is unknown, so the first step is to use the properties of probability distributions to write an equation that we can solve for the probability of one or more of the outcomes. Assign the variable x to the probability of rolling a 3, and compute the probabilities of the other outcomes, in terms of x. P(3) = x P(4) = P(5) = P(6) = = P(1) = P(2) = Substitute the probabilities, in terms of x, in to the probability distribution. Outcome 1 2 3 4 5 6 Probability 3x X