A fair coin is tossed six times. What is the probability that neither heads nor tails occur three times in succession?
2026-03-28 00:47:42.1774658862
problem regarding unbiased coin toss
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There are 64 possibilities in total.
3 consecutive heads: $2\cdot4+2\cdot2=12$
4 consecutive heads: $2\cdot2+1\cdot1=5$
5 consecutive heads: $2$
6 consecutive heads: $1$
The same can be done to tails, but be aware HHHTTT and TTTHHH are in both cases.
Therefore the probability is $\frac{64-38}{64}=\frac{13}{32}$