This is a question aimed at people newer to statistics/probabilities. I made this question as a test to myself because I haven't done stats in AGES.

A fair coin is thrown fairly 10, 20, 50, and 100 times.

What is the probability that the same side of the coin will not occur twice in a row.

Give the probability for each one.

(Or, if you're lazy, simply give a formula for finding the probabilities

EDIT: In answer to people's questions, this is to find out what people come up with, and maybe help somebody new to statistics who wants an easy question.