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17 March 2011 @ 05:13 pm
You'd think they'd check these problems more carefully...  
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.
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robszewczyk on March 18th, 2011 03:38 pm (UTC)
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.

jon_leonardjon_leonard on March 18th, 2011 04:17 pm (UTC)
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.