Heads in first three versus last two tosses

Question

Five fair coins are tossed one after another. What is the probability that the first three tosses contain the same number of heads as the final two tosses?

Short answer

$5/16$ . Match the count $r=0,1,2$ : $\sum_r \binom3r\binom2r/32=(1\cdot1+3\cdot2+3\cdot1)/32=\tfrac{10}{32}$ .

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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