Conditional Probabilityhard
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Let XX and YY be binary random variables representing the success of two independent server nodes. P(X=1)=pP(X=1) = p and P(Y=1)=qP(Y=1) = q. If we observe that the total number of successful nodes Z=X+YZ = X + Y is equal to 1, what is the conditional probability P(X=1Z=1)P(X=1 | Z=1)?