[rescue] Fun With Statistics

[David Cantrell]

On Sat, Jun 01, 2002 at 12:44:50PM -0400, Joshua D Boyd wrote:

[go me with the late reply!  I've not looked at my rescue mailbox for some
time]

> If you have events A and B, where P(A) and P(B) are the probabilities
> of that event happening, then
> P(A and B)=P(A)*P(B)
> P(A or B)=P(A)+P(B)

No.

With just two events, there are four possibilities:

not A and not B
A and B
A but not B
B but not A

and of course these four possibilities have a total probability of 1.

Now, P(A or B) == P(A, not B) + P(B, not A) - that's the exclusive or which
we usually mean in English.  If what you really want is "at least one of A
and B", then you want 1 - P(not A, not B), which is equivalent to:
  P(A, B) + P(A, not B) + P(B, not A)
but is a damned sight easier to spell :-)

Clearly, P(not A) = 1 - P(A) and likewise for B.

So, if P(A) = 0.1 and P(B) = 0.2, then the probability of a failure is 0.28.

It should be obvious that simply adding probabilities won't work, if you
consider the case where P(A) = 0.8 and P(B) = 0.6.  P(A) + P(B) = 1.4,
which is clearly bogus.

-- 
Grand Inquisitor Reverend David Cantrell | http://www.cantrell.org.uk/david

   It doesn't matter to me if someone else's computer is faster because
   I know my system could smash theirs flat if it fell over on it.
        -- (with apologies to Brian Chase)