easy Probability
A release-checked easy problem for training Exchangeability, Counting With Indicators, Linearity of Expectation, Combinations and Permutations.
$n$ heterosexual married couples ($1$ male and $1$ female) are standing in a line. They all scatter around and form $n$ pairs uniformly at random. Find the expected number of couples that are paired up together when $n = 8$. Pairs can consist of members of the same gender.
This Probability problem is tagged Exchangeability, Counting With Indicators, Linearity of Expectation, Combinations and Permutations. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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