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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.

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THey've used the binomial distribution where k=3,p=0.05 and n=4.

The Binomial distribution models the number of successes x in n repeated trials of a binomial experiment. It's actually 4C3 out the front, but that just equals 4.

What it's doing is calculating all the possible ways to get three amino acids (1/20)^3, then multiplying it by the possible ways of not getting those 3 amino acids (1-1/20)^(4-3). The reason they put 4C3 out the front is because out of 4 options they only want 3 matches. Then they multiply that with the previous parts.

EDIT: yes your answer about 0.05^4 is also correct, but have a look at plugging it into the binomial distribution--it will give you the same answer.

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