Does the named runner finish last?

Question

Five runners each finish with an independent time drawn from the same continuous distribution, so no two times tie.

What is the probability that one particular runner, say Runner C, posts the slowest time of the five?

Accepted Answer

The slowest time is the maximum of the five. Since all five times come from the same distribution and are independent, each runner is equally likely to be the slowest. Runner C is just one of five equally likely candidates: \frac{1}{5} = 0.2. Takeaway. Being slowest is the same symmetry problem as being fastest: any one of n exchangeable competitors holds a given extreme with probability 1/n.

Does the named runner finish last?

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