371.Tails Come in Pairs
★★★combinatoricsCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
A fair coin is flipped 10 times. Find the probability that tails only occur in consecutive pairs — i.e., every maximal run of tails has even length. (With 4 flips: , , are valid; is not.)
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Valid sequences are exactly tilings of a length-10 strip by tiles (length 1) and tiles (length 2).
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