GATE 2015 CS (CS3) – Question 61
X1,X2,X3 are independent, each equally likely zero or one. Y=(X1X2) XOR X3, where juxtaposition denotes multiplication. Find P(Y=0 | X3=0).
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Correct answer: 0.75
Explanation
Conditioning on X3=0 makes Y equal to X1X2. Independence leaves X1 and X2 fair under this conditioning. Their product is one only when both are one, probability one quarter; therefore it is zero with probability three quarters. The answer is 0.75.