Question

Suppose each of two boxes contains two identical balls marked with numbers 1 and 2. Two balls are selected at random, one from each box simultaneously. Let X denote the maximum of the numbers on the balls selected and Y the minimum of the numbers on the balls selected. Determine the joint probability distribution of X and Y

Answer 1

P(X=1, Y=1) = P{both time selected 1} = 0.5*0.5 = 0.25

P(X=1, Y=2) = P{max is 1, min is 2} = 0

P(X=2, Y=1) = P{exactly one time selected 2} = 2 * 0.5 * 0.5 = 0.5

P(X=2, Y=2) = P{both time selected 2} = 0.5 * 0.5 = 0.25