EXERCISE

12.2.1:The probability of an event - coin flips.

A fair coin is flipped n times. Give an expression for each of the probabilities below as a function of n. Simplify your final expression as much as possible.

(a)

At least n - 1 flips come up heads.

(b)

There are at least two consecutive flips that are the same.

(c)

The number of heads is different from the number of tails. (Assume that n is even, otherwise the probability is one.)