Class summary: Monday, 3/3

I concluded the interlude on combinatorial probabilities by discussing a rather famous problem, the so-called matching problem. One version of this problem is the "hat check problem", which involves n guests at a party whose hats get mixed up; the problem is to compute the probability that nobody gets their own hat back. This is equivalent to asking for the probability that in a random permutation of the numbers 1,2,...,n no number remains in its original position. The solution to this problem is an illustration of the inclusion-exclusion formula which generalizes the familiar formula for P(A1 union A2) = P(A1)+P(A2) - P(A1 intersect A2) to unions of n events.

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