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Conditional Probabilityhard
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Let XXX and YYY be independent discrete random variables such that P(X=k)=13P(X=k) = \frac{1}{3}P(X=k)=31​ for k∈{1,2,3}k \in \{1, 2, 3\}k∈{1,2,3} and P(Y=m)=12P(Y=m) = \frac{1}{2}P(Y=m)=21​ for m∈{1,2}m \in \{1, 2\}m∈{1,2}. Find P(X+Y≤3∣X⋅Y≤3)P(X+Y \leq 3 | X \cdot Y \leq 3)P(X+Y≤3∣X⋅Y≤3).