Conditional Probabilityhard
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Let XX and YY be two independent discrete random variables taking values in {1,2,3}\{1, 2, 3\}. Suppose P(X=k)=1/3P(X=k) = 1/3 and P(Y=k)=1/3P(Y=k) = 1/3 for all kk. Define M=max(X,Y)M = \max(X, Y). What is P(X=1M=2)P(X=1 | M=2)?