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**Consider an experiment that consists of 2 rolls of a balanced die. If X is the number of 4s and Y is the number of 5s obtained in the 2 rolls of the die, find the joint probability function.**

[tex]f(x,y) = \frac{(_{2}C_{x})(_{2}C_{y})}{36}[/tex]

because there are [tex]_{2}C_{x}[/tex] ways to combine x 4s and [tex]_{2}C_{y}[/tex] ways to combine y 5s, and 36 possible combinations from a throw with 2 dice.

However, this formula doesn't give me the correct probability distribution of X and Y. What's my mistake?