medium Probability
A release-checked medium problem for training Linearity of Expectation.
There are $n$ people in a probability class. Each person is equally likely to be born on any day of the $365$ days in a year. Compute the expected number of groups of $2 \leq k \leq n$ people that have the same birthday when $n = 25$ and $k = 4$. Round to the nearest hundred-thousandth.
This Probability problem is tagged Linearity of Expectation. 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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