Spouses seated side by side at a round table

Question

Four married couples (eight people) are seated at random around a circular table with eight seats. What is the expected number of couples who end up in adjacent seats?

Short answer

$8/7$ . For a given person, the spouse is equally likely to occupy any of the other 7 seats, 2 of which are adjacent, so each couple is together with probability $\tfrac27$ . Linearity gives $4\cdot\tfrac27=\tfrac87$ .

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Lessons behind this question

Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited
Sample Spaces, Events, and the Probability Axioms

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