Joint Probability. An example with the Solution.

Problem: Each throw of an unfair die lands on each of the odd numbers 1, 3, 5 with probability 1/9 and on each of the even numbers with probability 2/9. Suppose that the die is tossed. Let X equal 1 if the result is an even number, and let it be 0 otherwise. Also, let Y equal 1 if the result is a number greater than three and let it be 0 otherwise. Find the joint probability mass function of X and Y.