Question

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

Answer 1

would they we dependent or independent

Answer 2

dependent

Answer 3

okay. thank you

Answer 4

your welcome anytime

Answer 5

would that be the same as disjoint?

Answer 6

hold the phone!

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

no

Answer 12

disjoint means there is nothing in \(A\cap B\)

Answer 13

oh okay!

Answer 14

sets are not equal to zero
probabilities are equal to zero

Answer 15

this makes my next problem easier

Answer 16

thank you so much

Answer 17

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

Answer 18

yw

Answer 19

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