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Suppose X and Y are independent and identically distributed random variables that are distributed uniformly in the interval [0,1]. The probability that X ≥ Y is _______.

1. 1/2
2. 1/3
3. 2/3
4. 1

Correct answer: 1/2

Solution

Since X and Y are uniformly distributed over the same interval and are independent, the area where X is greater than or equal to Y is exactly half of the total area of the unit square formed by their possible values. Thus, the probability that X is greater than or equal to Y is 1/2.

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