Question 10
Bob writes a random string of 5 letters, where each letter is either $A$, $B$, $C$, or $D$. The letter in each position is independently chosen, and each of the letters $A$, $B$, $C$, $D$ is chosen with equal probability. Given that there are at least two $A$'s in the string, find the probability that there are at least three $A$'s in the string.