I thought of this as I'm reading about covid tests accuracy, and I am thinking how taking multiple tests influences the chance of correctly detecting illness/no illness. So, if I understand this concepts correctly, I want to see how specificity and sensitivity change (and I assume they increase) when taking two tests.
I'm going to denote testing positive with + and having the illness as I, not having as NI. I'm going to limit the question to seeing one positive test result vs seeing two.
Then since P(++)=P(+)*P(+) as events are independent, I have
and now I'm not sure where to take it, and how Bayes theorem was even useful. It seems I am missing something. I think I also need the prevalence of the disease in the general population to compute this, that is, P(I).