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Question
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, ...., n}. Find P[r ≤ p|s ≤ p], where p ∈ S.
Solution
Given that: S = {1, 2, 3, ..., n}
∴ P(r ≤ p|s ≤ p) = `("P"("P" ∩ "S"))/("P"("S"))`
= `("p" - 1)/"n" xx "n"/("n" - 1)`
= `("p" - 1)/("n" - 1)`
Hence, the required probability is `("p" - 1)/("n" - 1)`.
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