Calculate the probability that if a DNA chain of length 5 is chosen at random, it will have at least four A’s.

There are a total of \(4^5 = 1024\) outcomes. We are interested in chains that have 4 or 5 A’s. Those can be formed in \(\binom{5}{4} \cdot 3 + \binom{5}{5} = 16\) ways so the probability is \(\frac{\binom{5}{4} \cdot 3 + \binom{5}{5}}{4^5} = \frac{16}{1024} = \frac{1}{64}\)