Calculate the chance that an allele is not sequenced?

Hello,

With 30X depth NGS sequencing, what is the chance at one position that an allele is not sequenced at all with 30 reads ?

Should we do 2^30 = 1 073 741 824 ?

Thank you.

The probability is a number between 0 and 1, so by definition it cannot be 2^30.
However, I think you were close.

First of all: I assume you want to know the probability that, in a heterozygous individual, sequencing 30 reads, you always sequence allele 1 and never allele 2.

Each read has a 0.5 probability of sequencing allele 1, and 0.5 of sequencing allele 2. The probability that with 2 reads you always sequence allele 1 is 0.5 * 0.5 (0.5^2), with 3 is 0.5^3, and so on… thus the probability that with 30 reads you always sequence allele 1 is 0.5^30, i.e. 9^-10.

I hope this helps