Problem: A piece of string is cut in two at a point selected at random. The probability that the longer piece is at least times as large as the shorter piece is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let represent the string (See figure) and let be the point on it such that . If has length a incbes, then the length of is . The probability that the cut lie on is . Since the cut is equally likely to lie within the same distance from the other end of the string, the probability of either is of choice ( E ).
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