What must be true in order for P (A or B) = P(A) + P (B)?

Question

anonymous · Answer

would they we dependent or independent

goldeverything · Answer

dependent

anonymous · Answer

okay. thank you

goldeverything · Answer

your welcome anytime

anonymous · Answer

would that be the same as disjoint?

anonymous · Answer

hold the phone!

anonymous · Answer

here are my options
A and B cannot be disjoint. 
 A and B must be independent. 
 A and B cannot be independent. 
 A and B must be disjoint. 
 It is always true.

anonymous · Answer

it has nothing to do with "independence" at all
if $P(A\cup B)=P(A)+P(B)$ then $P(A\cap B)=0$

anonymous · Answer

if $P(A\cap B)=0$ then in most cases $A\cap B=\emptyset$ and so $A$ and $B$ are "disjoint"

anonymous · Answer

what does disjoint even mean? does it mean equal to 0?

anonymous · Answer

no

anonymous · Answer

disjoint means there is nothing in $A\cap B$

anonymous · Answer

oh okay!

anonymous · Answer

sets are not equal to zero
probabilities are equal to zero

anonymous · Answer

this makes my next problem easier

anonymous · Answer

thank you so much

anonymous · Answer

example, if $A=\{a,b\}$ and $B=\{c,d\}$ then $A\cap B=\emptyset$ i.e. there is nothing in the intersection

anonymous · Answer

yw

anonymous · Answer

oh okay, just to clarify, What would happen with the same problem if I multiplied p(a) and p(b)