Example 4.4.5: Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 5 are all equal, but the probability of rolling a 6 is twice the probability of roll- ing a 1. When you roll the die once, the 6 outcomes are not equally likely. What are the probabilities of the 6 outcomes?
On the basis of the above question a question has been asked to evaluate the mean.
My problem is that, when they evaluate the mean, they multiplied with the probability by 1, 2 , 3 , 4 , 5 and 6 why? In die , all are they equal probable.