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 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).