You'd think they'd check these problems more carefully...

[jon_leonard]

I was just working with a student, and they had a probability problem where:

P(A or B) = 1/2, but P(B) = 3/4

This really isn't a context where P(A and not B) is allowed to be -1/4.

Comments

[robszewczyk]

is there such a context?

related, I was running a probability calc recently, and determined it probably needed debugging when it came up with a P(X) = 2034.

--Beth

[jon_leonard]

There do seem to be some such contexts: Negative Probability (at Wikipedia).

I was vaguely aware that they turned up in quantum mechanics; my limited understanding at this point is that when you have two events that interfere with each other, it's sometimes useful to consider how much additional likelihood the event B adds as compared to A alone. But if B makes A less likely, that looks like a negative probability. I should probably study this more, and continue not mentioning it to students.