Two natural numbers r, s are drawn one at a time, without replacement

1.	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» Given, S = {1, 2, 3, …, n} So, P(r ≤ p/s ≤ p) = P(P ⋂ S)/ P(S) = p – 1/n x n/(n – 1) = (p – 1)/(n – 1) Therefore, the required probability is (p – 1)/(n – 1).

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»

Given, S = {1, 2, 3, …, n}

So, P(r ≤ p/s ≤ p) = P(P ⋂ S)/ P(S)

= p – 1/n x n/(n – 1)

= (p – 1)/(n – 1)

Therefore, the required probability is (p – 1)/(n – 1).

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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.

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