## anonymous 3 years ago how are disjoint and independent different

1. Zarkon

Two events A and B are disjoint if $$A\cap B=\emptyset$$ A and B are independent if $$P(A\cap B)=P(A)\times P(B)$$

2. anonymous

thanks

3. anonymous

so if A and B were disjoint P(A U B)= P(A)+P(B) ?

4. Zarkon

another way to look at it if A and B are disjoint...then if I know event A occurs then that means that B cannot occur..thus A and B are dependent (provided their individual probabilities are nonzero)

5. Zarkon

yes

6. anonymous

I will remember that" when it is disjoint it is not independet"

7. Zarkon

correct...provided the nonzero probabilities

8. anonymous

ok

9. Zarkon

since if P(A)=0 then $$P(A\cap B)=0$$ and thus $0=P(A\cap B)=P(A)\times P(B)=0\times P(B)=0$