Question

how are disjoint and independent different

Answer 1

Two events A and B are disjoint if \(A\cap B=\emptyset\)

A and B are independent if \(P(A\cap B)=P(A)\times P(B)\)

Answer 2

thanks

Answer 3

so if A and B were disjoint

P(A U B)= P(A)+P(B)

?

Answer 4

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)

Answer 5

yes

Answer 6

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

Answer 7

correct...provided the nonzero probabilities

Answer 8

ok

Answer 9

since if P(A)=0 then \(P(A\cap B)=0\)

and thus

\[0=P(A\cap B)=P(A)\times P(B)=0\times P(B)=0\]