Four people each place their hat into a box. The hats are shuffled and each person draws one at random. What is the expected number of people who draw their own hat?
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Let Xi=1 if person i draws their own hat. Then E[Xi]=41. By linearity of expectation, E[X1+X2+X3+X4]=4⋅41=1. Remarkably, this equals 1 regardless of how many people participate.