In Shapiro et al., when discussing about loss of molecules as source of error in single-cell sequencing, it is written that:
Another source of error is losses, which can be severe. The detection limit of published protocols is $5$–$10$ molecules of mRNA. If, as seems likely, the limit of detection is primarily determined by losses during sample preparation, this would indicate that $80$–$90\%$ of mRNA was lost. Or, to put it the other way around, a $90\%$ loss leads to an approximately $50\%$ chance of failing to detect a gene that is expressed at a level of seven mRNA molecules (from the binomial distribution).
How is this probability computed using the binomial distribution? I thought that $90\%$ loss corresponds to $5$ detected molecules, and I assume that $k=7$ for the binomial calculation, but I am unable to go further.