Probability that a word contains at least 3 same consecutive letters? Assume we have a word of length $n$ and an alphabet of length $26$ (the small letters a through z, if you want so.
How likely is it that this word contains at least $k := 3$ consecutive letters of any type?
Examples that match:
aaabababab 
aoeuuuuuuu
aaaaaaaaaa

Examples that do not match:
ababababab
banananana
abcdefghij


Use the binomial cumulative distribution function with probability of $\frac 1{26}$ to find the probability of having at most a sequence of two duplicate letters out of $n$. You are looking for $1-P(x \leq 2)$
