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.

Answer 1

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)`.