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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