Problem:
Four distinct points, , and , are to be selected from 1996 points evenly spaced around a circle. All quadruples are equally likely to be chosen. What is the probability that the chord intersects the chord
Answer Choices:
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E.
Solution:
Because all quadruples are equally likely, we need only examine the six clockwise orderings of the points: , and . Only the first two of these equally likely orderings satisfy the intersection condition, so the probability is .