Probability

How many sequences of  five flips satisfy the conditions, and have the third flip be heads?
We have _ _H _ _: So exactly one of the first two flips is heads, and exactly one of the last two flips is
heads. This gives 2 × 2 = 4 possibilities.

How many sequences of five flips satisfy the conditions, and have the third flip be tails?

Now we have  _ _ T _ _ :  so the first two and the last two flips must all be heads. This gives only 1 possibility.

So the probability that the third flip was head is 4/ ( 4+1) = 4/5 .