1972 AHSME Problems/Problem 17

Problem 17

A piece of string is cut in two at a point selected at random. The probability that the longer piece is at least x times as large as the shorter piece is

$\textbf{(A) }\frac{1}{2}\qquad \textbf{(B) }\frac{2}{x}\qquad \textbf{(C) }\frac{1}{x+1}\qquad \textbf{(D) }\frac{1}{x}\qquad \textbf{(E) }\frac{2}{x+1}$

Solution

The string could be represented by a line plot segment on the interval $(0,x+1)$ . The interval $(0,1)$ is a solution as well as $(x,x+1)$ . The probability is therefore $\boxed{\textbf{(E) }\frac{2}{x+1}}.$ ~lopkiloinm

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1972 AHSME Problems/Problem 17

Problem 17

Solution