Consider a permutation sampled uniformly at random from the set of all…

2024

Consider a permutation sampled uniformly at random from the set of all permutations of {1, 2, 3, ⋯ , 𝑛} for some 𝑛 ≥ 4. Let 𝑋 be the event that 1 occurs before 2 in the permutation, and 𝑌 the event that 3 occurs before 4. Which one of the following statements is TRUE?

  1. A.

    The events 𝑋 and 𝑌 are mutually exclusive

  2. B.

    The events 𝑋 and 𝑌 are independent

  3. C.

    Either event 𝑋 or 𝑌 must occur

  4. D.

    Event 𝑋 is more likely than event 𝑌

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