What is the likelihood that two peptides with a length of 8

What is the likelihood that two peptides with a length of 8 amino acids have exactly the same sequence?

Solution

if we consider the total standard aminoacids i.e the amino acids that are frequently appeared in the proteins are 20. Then Probability = No. of times an event occur / Total No. of events

Here, Probability for 1 amino acid same in the octa peptide: 1/20

Similarly Probability of 8 amino acids same in the octa peptide: (1/20)^{8 =} 1/400 x 1/400 x 1/400 x 1/400

= 0.0025 x 0.0025 x 0.0025 x 0.0025

= 3.90625e^-11

By using Multiplicative law or And rule of probability