Probability lesson

["Raymond DeCampo" <rkdecamp@mailbox.syr.edu>]

Hi guys,

Recently somebody wrote that the prob Boston getting the first pick 
was 27.3% and the prob of Dallas was 8.7%.  They then concluded that 
the prob for the C's to end up with the first pick is 27.3+8.7=36%.
This is correct.

Another poster pointed out that usually you must be more careful when 
adding probabilities.  He was referring (I beleive) to an occaision 
where somebody had tried to calculate the odds of the C's ending up 
with at least one of the first three picks.  He did this by adding 
the odds of them getting any of the picks individually.  This was 
incorrect.

So how do you know how to add probabilities?  Good question.  Suppose 
you are looking at two events E and F.  Suppose we would like to know 
the probability of E or F.  This is given by the simple formula:

prob(E or F) = prob(E) + prob(F) - prob(E and F)

So if E=Boston winning the lottery and F=Dallas winning the lottery 
then both E and F cannot happen.  So prob(E and F)=0 and that's why 
the first poster I mentioned was correct.

If however we are talking about E=the Celtics ending up with the first 
pick  and F=the C's ending up with the second pick then it is 
possible to have E and F happen.  So that is why the second poster 
was incorrect.

I hope that clears everything up.  As you can see probability can be 
counter-intuitive even at a basic level.  It has tripped up many an 
intelligent person!

Ray