What is the probability that the median of three randomly, Mathematics

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What is the probability that the median of three randomly

One idea that is often used in selection is that instead of choosing a random pivot element, we choose three random pivot elements and then use the median of these three as our pivot. What is the probability that a randomly chosen pivot element is in the middle half? What is the probability that the median of three randomly chosen pivot elements is in the middle half? Does this justify the choice of using the median of three as pivot?

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