Question

In a barn, 100 chicks sit peacefully in a circle. Suddenly each chick randomly pecks each chick from its left or right. What is the expected number of unpecked chickens?

Answer 1

For any chick, there is a 0.5 chance that the one on its right won't peck it, and a 0.5

chance that the one on its left won't peck it. So overall, it has a 0.5*0.5=0.25 chance of not being pecked.

Thus, we expect that among 100 chicks 25 will be unpecked.