swerve wrote:A tightrope approximately 320 m long is suspended between two poles. During a performance, a break occurs in the line. Assume that the line has an equal chance of breaking anywhere along its length. What is the probability that the break happened in the first 50 meters of the rope?
A. \(\frac{27}{32}\)
B. \(\frac{1}{2}\)
C. \(\frac{5}{32}\)
D. \(\frac{5}{27}\)
E. \(\frac{2}{3}\)
The OA is C
Source: Economist GMAT
Since the rope has an equal chance of breaking anywhere along its length, theoretically there are infinite number of points at which it can break. However, for the sake of the question, let's assume that per meter length there are n points at which it can break. So, for the 320 meters, there are 320n points and in the first 50 meters, there are 50n points.
Thus, the probability that the break happened in the first 50 meters of the rope = 50n/320n = 5/32.
The correct answer:
C
Hope this helps!
-Jay
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