MathCastle
Counting & ProbabilityChallengeExpected Value, Linearity & Advanced Probability

Expected Value, Linearity & Advanced Probability · Challenge problem

Five couples (1010 people) are seated uniformly at random around a round table with 1010 seats. Find the expected number of couples seated in adjacent seats.

The answer is a fraction mn\tfrac{m}{n} in lowest terms; find m+nm + n.