What Does P(A or B but Not Both) Represent in Probability?

[denian]

what does this mean?

P (A or B but not both ( A and B ) ) ?

does it mean
P (A U B ) - P (A intersect B )?

 

[Wong]

Yes that is correct. By the way, do you know how to draw "Venn's diagram"? That would make things a bit easier.

 

[denian]

i ask that question because i see my friend work
she said it means

P ( A U B ) - 2 P ( A intersect B )

and she get the answer.

 

[Wong]

Ok, I think it means P(A)+P(B)-2P(A intersects B).

 

[denian]

thats it. thanks.

 

[maverick280857]

I believe your problem is essentially solved but it is helpful to construct Venn diagrams in such situations (as Wong suggested) to make some useful generalizations. Set theoretically, A or B but not not both A and B means that the region in the venn diagram that is common to both A and B is excluded (of course, the region described by the sample space - (A+B) is also excluded). This translates (in the "only" notation) to,

$$(A only) \bigcup (B only)$$

which really is

$$(A \bigcap B') \bigcup (A' \bigcap B)$$