Since the outcomes are equally likely, the values of p(x,y) are found by counting the number of outcomes in the sample space Ω that result in the specified values of the random variables,...Since the outcomes are equally likely, the values of p(x,y) are found by counting the number of outcomes in the sample space Ω that result in the specified values of the random variables, and then dividing by 8, the total number of outcomes in Ω. In the above, we use the idea that if X and Y are independent, then the event that X takes on a given value x is independent of the event that Y takes the value y.
