1. ## independence

Hi, im just confirming if this logic is right, for my assignment. Well i know that events are mutually exclusive if $P (A \cap B) = 0$. And then this is not independent.

so if i wanted to determine is something is independent then is it just if $P (A \cap B)$ is not equal to 0?

coz in this subject we havent covered stuff like chi-squares so im not allowed to do that. thanks

2. Originally Posted by Katina88
Hi, im just confirming if this logic is right, for my assignment. Well i know that events are mutually exclusive if $P (A \cap B) = 0$. And then this is not independent.

so if i wanted to determine is something is independent then is it just if $P (A \cap B)$ is not equal to 0?

coz in this subject we havent covered stuff like chi-squares so im not allowed to do that. thanks
The test for the independence of two events is clearly stated here: http://en.wikipedia.org/wiki/Indepen...ability_theory)

3. ok then is this right:
if
$P(A|B) = P(A|B') = P(A)$ then it is independent?

4. Originally Posted by Katina88
ok then is this right:
if
$P(A|B) = P(A|B') = P(A)$ then it is independent?
Yes. But the condition $\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)$ might be the better one to apply.

5. Originally Posted by mr fantastic
Yes. But the condition $\Pr(A \cup B) = \Pr(A) \cdot \Pr(B)$ might be the better one to apply.

OMG that's a BAD typo
you mean intersection and not union here.
Another clarification...
Mutually exclusive or disjoint means that the intersection of two sets is empty,
THAT implies that P(AB)=0.
BUT P(AB)=0 does not mean they are disjoint.

Also If two sets are independent then..........

$P(A|B)=P(A)=P(A|B')$
and
$P(B|A)=P(B)=P(B|A')$
and
$P(AB)=P(A)P(B)$
and
$P(AB')=P(A)P(B')$
and
$P(A'B)=P(A')P(B)$
and
$P(A'B')=P(A')P(B')$

IF any one hold, ALL HOLD.
And if one fails, they all do.

NOW to the question at hand, which I did in class 2 weeks ago.
IF A and B are disjoint (and they have positive probability) then they are dependent.

That's because P(AB)=0 while P(A)P(B)>0, so

$P(AB)\ne P(A)P(B)$

6. Originally Posted by Katina88
ok then is this right:
if
$P(A|B) = P(A|B') = P(A)$ then it is independent?
If $P(A|B) = P(A)$ they are independent

It then follows that $P(A|B') = P(A)$ too.

You only need show that 2 of these 3 are equal
$P(A|B) = P(A|B') = P(A)$
the other must also be equal to the first two.

These are the more intuitive definitions.
IF A and B are independent then knowing one does not change the probability of the other.
$P(A|B)=P(A)$

7. Originally Posted by matheagle
OMG that's a BAD typo
lol i was thinking that i was doing something wrong. hehe thanks

8. night