Consider a permutation sampled uniformly at random from the set of all…
GATE · 2024 · CS · Set 1 · Computer Science & IT
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?
- A.
The events 𝑋 and 𝑌 are mutually exclusive
- B.
The events 𝑋 and 𝑌 are independent
- C.
Either event 𝑋 or 𝑌 must occur
- D.
Event 𝑋 is more likely than event 𝑌
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