Two natural numbers r, s are drawn one at a time,

Question:

Two natural numbers rare drawn one at a time, without replacement from the set S={1, 2, 3, …., n} . Find P[£ p|£ p] , where pÎS.

Solution:

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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