I have a specific question about this problem.
Problem statement summary:
8 men, 7 women, what's the expected number of male female or female male couples sitting directly adjacent to each other sitting in 15 seats?
My question:
The answer uses the fact that expectation is linear and you simply need to calculate E(MF), E(FM) from the first two seats and multiply by the number of possible adjacent pairs.
Why exactly is expectation linear? Does anyone have an intuitive explanation? The other examples on stack exchange just quote the formula without much of an explanation.
It seems like the probability of a male female or female male couple changes depending on how many are seated already?
Thanks in advance for any answers.
