What is the probability that a sequence of seven flips of a fair coin turns out to be exactly HTHTTHH?

Answer 1

There are 2⁷ = 128 possibilities, and all are equally likely since the coin is fair. So the probability of this particular sequence is 1/128.

If this is still a bit confusing, it may help to build up to seven flips. Think about the following simpler questions:

1) What is the probability that a single flip of a fair coin turns out to be exactly H?

2) What is the probability that a sequence of two flips of a fair coin turns out to be exactly HT?

3) What is the probability that a sequence of three flips of a fair coin turns out to be exactly HTH?

4) What is the probability that a sequence of four flips of a fair coin turns out to be exactly HTHT?