Suppose you have a suit of events A1, A2, A3 ... An, that correlate with event B with varying strength. You want to calculate the aposteriory probability of B using the Bayes theorem, and obtain a set of numbers. How do you decide which one is the correct one? Or you just must do these calculations several times and then pick the best indicator? Sorry, I suspect there is a simple answer...
Are you trying to find the probability of B given all n events, that is, Pr[B|A1, A2, ..., An]? In that case, none of the calculations Pr[B|A1], Pr[B|A2], ..., Pr[B|An] are useful, necessarily. In fact, even if each Ai individually makes B more likely, together they may make B less likely.
(For example, suppose we are rolling a fair 6-sided die, and take A1 = "We get 1 or 3", A2 = "We get 2 or 3", and B = "We get 1 or 2". Then Pr[B] = 1/3 before we condition, since 2 out of 6 outcomes satisfy B. If we learn either A1 or A2, th...
I think it's past time for another Stupid Questions thread, so here we go.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Please respect people trying to fix any ignorance they might have, rather than mocking that ignorance.