I'm trying to understand the notes from my bioinformatics lecture and I have some issues with calculation the probabilities: What is the probability that at least 3 amino acids match in two sequences of lenght 4? So I know that there can be 4 possible combinations which can occur so there are 3 matches and probability of one particular amino acid is 1/20. In the lecture notes there was this formula:
p = (1/20)^3 * (1-1/20)^1 * 4
I understand everything except the times 4 at the end. When those are two sequences compared (like rolling two dice 4 times and get 3 times the same number) shouldn't it be without the times 4?
And if wanted to calculate the probability that all four would match then I would just do:
p = (1/20)^4
Is that correct? Thank you very much for help.