Question

Pr(A/B)=0 means Pr(AintersectsB)=0? True or False?

Answer 1

i would say true

Answer 2

How do you know?

Answer 3

\(P(A|B)\) is the probability that A occurs given that B has occurred. if the intersection is empty, then if B occurred A cannot.
i can actually think of a strange example where this is not actually true, but i think you are supposed to say yes

Answer 4

if you are taking a basic probability class you should maybe say yes, the intersection must be empty, but i can give you a counter example, so show that it is not necessarily true if you like

Answer 5

No, I understand now. Thank you. That makes a lot of sense. So does probability (A) mean that A and B are not independent?

Answer 6

let \(A=[0,1]\cup \{\frac{3}{2}\}\) and \(B=[1,2]\) and the experiment is to pick a number at random on the interval \([0,2]\)
then \(A\cap B=\{1,\frac{3}{2}\}\) but \(P(A|B)=0\)

Answer 7

independent means \(P(A|B)=P(A)\)

Answer 8

so yes then?

Answer 9

I think...

Answer 10

the example i wrote above is a counter example, i.e. it disproves that \(P(A|B)=0\implies A\cap B=\emptyset\)

Answer 11

but i do not mean to confuse you, so maybe you should ignore my example and just say "yes" which is i probably what your teacher wants, although maybe i am wrong about that.

Answer 12

But a basic probability class would say true despite a couple of exeptions?

Answer 13

*exceptions

Answer 14

yes , especially if you are working with discrete probability
what level of class is this?

Answer 15

Would my second question be true then too? I said it was true. and Finite math freshman in college

Answer 16

if it is "finite math " then my guess is say yes.
i am not sure what the second question is.
"independent' refers to two sets. you say A and B are independent if \(P(A|B)=P(A)\) or in plain english, knowing that B has occurred gives no information about whether A will occur.
example: flip two coins. the fact that the first one lands heads gives no information about whether it is more or less likely that the second one lands heads

on the other hand if \(P(A|B)=0\) and \(P(A)\neq 0\) then A and B must be dependent

Answer 17

Thank you so much, I definitely understand with those clear examples. I'm preparing for my final and I realize I have forgotten a lot.
So, if Pr(A/B)=0 means Pr (A intersection B)=0 is True right? just clarification