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Probability of choosing n, n>50, is 3p

Source: 1978 AHSME Problem 19

June 6, 2014
probabilityAMC

Problem Statement

A positive integer nn not exceeding 100100 is chosen in such a way that if n≤50n\le 50, then the probability of choosing nn is pp, and if n>50n > 50, then the probability of choosing nn is 3p3p. The probability that a perfect square is chosen is
<spanclass=′latex−bold′>(A)</span>.05<spanclass=′latex−bold′>(B)</span>.065<spanclass=′latex−bold′>(C)</span>.08<spanclass=′latex−bold′>(D)</span>.09<spanclass=′latex−bold′>(E)</span>.1<span class='latex-bold'>(A) </span>.05\qquad<span class='latex-bold'>(B) </span>.065\qquad<span class='latex-bold'>(C) </span>.08\qquad<span class='latex-bold'>(D) </span>.09\qquad <span class='latex-bold'>(E) </span>.1
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