Say that we have a coin (p, the probability of heads, is unknown), and will toss it five times, and if it comes up heads all five times, decide that it is biased in favor of heads. Otherwise (when number of heads in five tosses is four or less) we will decide that the coin is fair.

When p is 0.8 (so the coin is very biased), is it possible to decide that the coin is fair? If so, what is the probability of that?