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Larger of two numbers chosen from the first n natural numbers: expected value

This type of question, asked 2 times: 20 Apr 2025 S2, 14 May 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    143
    Two numbers are selected at random, without replacement from the first 6 positive integers. Let X denote the larger of the two numbers. Then E(X)=E(X) =

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  2. Question 2

    14 May 2026 S2

    100
    Two numbers are selected at random without replacement from the first nn natural numbers. Let X denote the larger of the two numbers obtained. If E(X)=143E(X) = \dfrac{14}{3}, then the value of nn is

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