Making sense of genotype calculation equations

I am struggling understand the first two of the following equations, which are from the Supplementary materials of the Conpair paper, and describe how genotypes are calculated:
Conpair equations

For the first equation, the probability of D|AA is much lower if all my reads were A compared to if all my reads were B? Is e_j what I think it means? I would think a low e_j means that the call is more reliable. Ex: my error rate is .01 and D={A,A,A,A}:

P(D|AA) = (.01^4)(.99^0)=1e-8

But if D={B,B,B,B}, the calculation comes to:

P(D|AA) = (.01^0)(.99^4) ~ .96

For the second equation, the occurrences of A are not considered at all? The index and upper bound for both operators are exactly the same, if I’m reading that right? Is it just me or are there a bunch of typos here?

Bergmann EA, Chen BJ, Arora K, Vacic V, Zody MC. Conpair: concordance and contamination estimator for matched tumor-normal pairs. Bioinformatics. 2016 Oct 15;32(20):3196-3198. doi: 10.1093/bioinformatics/btw389. Epub 2016 Jun 26. PMID: 27354699; PMCID: PMC5048070.

Read more here: Source link