Chris tries to throw a ball of paper in the wastebasket behind his back (without looking). He estimates that his chance of success each time, regardless of the outcome of the other attempts, is 1/3. Let X be the number of attempts required. If he is not successful within the first 5 attempts, then he quits, and he lets X = 6 in such a case.
Let Y indicate whether he makes the basket successfully within the first three attempts. Thus Y = 1 if his first, second, or third attempt is successful, and Y = 0 otherwise.
Find the conditional mass of X given Y. You will need to list 12 values altogether, i.e., you need to compute Px|y(x | y) for 1 < x < 6 and 0 < y < 1.