I saw a picture saying something along the lines of "Alice is sick, Bob is healthy. If Alice doesn't wear a mask, and Bob does, there is a 70% probability of transmission. If Alice wears a mask and Bob doesn't, there's a 5% chance of transmission. If Alice and Bob wear masks, there is a 1.5% chance of transmission"
This got me to thinking, "what if both don't wear masks?"
So the known stuff is P(T|~A&B) = 70%, P(T|A&~B) = 5%, and P(T|A&B) = 1.5%. And to find P(T|~A&~B), I'd use bayes theorem. But I can't figure out how to apply it. I think we assume Alice and Bob wearing masks is independent, so P(A&B) = P(A)*P(B). But I don't know if I can pull that out of a "given" statement. That is to say, can we assume P(A&B|T) = P(A|T)&P(B|T)?