GATE 2021 ST – Question 25

Probability · Events and Conditional Probability · 1 mark · Numerical answer

A fair die is rolled twice independently,giving X,Y. Find E[X+Y | (X−Y)²=1].

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Correct answer: 7 to 7

Explanation

The condition means adjacent outcomes. The ten equally likely ordered pairs are (1,2),(2,1),…,(5,6),(6,5),with sums 3,5,7,9,11 each occurring twice. Their conditional average is (3+5+7+9+11)/5=**7**.

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