Are you smarter than a 13y/o?

...

0

N where N is defined as the answer to that question

50

0

25? Assuming each chick has a 25% chance of not getting pecked by either peer.

25

Every chick has a 50% chance of being peck by the one on its left and 50% by one on its right

At most there can be 2 unpecked chicks and the expected number tends to that as you increase the number of chicks or you move the probability distribution of pecking left and right closer to 50/50. If the distribution were 100/0 there would be 0 unpecked chicks every time for example.

There you go. This took me half a second, thus making me smarter than the 13 year old.

25

Each chick in the circle has a 50% chance of being pecked by the chick on its left and a 50% chance of being pecked by the chick on its right right.

The probability that a chick gets pecked is then

.50 + .50 - (.50)(.50) = .75

This probability is the same for every chick and so the expectation value of each chicken getting at least one peck is just (1*.75)(100) = 75

and the expected number of unpecked chicks is 1-75 = 25