Suppose a coin is tossed 21 times in a row with equal probability of heads and tails
a. What is the probability that heads does not occur three times in a row?
That is, with 21 tosses, what is the probability heads is never immediately
followed by two other heads?

b. What is the probability that the coin is facing the same way three times in
a row (that is three heads in a row or three tails in a row) exactly once in
the 21 tosses?