Is the biggest draw among the first two?

Question

You take 6 independent draws from the same continuous distribution, one after another, so no two are equal. What is the probability that the largest of the six draws is one of the first two you took?

Accepted Answer

Each of the six draws is equally likely to be the maximum, by symmetry. The event "the maximum is among the first two" covers exactly two of those six equally likely spots: \frac{2}{6} = \frac{1}{3} \approx 0.333. Takeaway. The chance the maximum lands in a chosen block of k out of n exchangeable draws is just k/n.

Is the biggest draw among the first two?

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