Hi, im just confirming if this logic is right, for my assignment. Well i know that events are mutually exclusive if . And then this is not independent.
so if i wanted to determine is something is independent then is it just if is not equal to 0?
coz in this subject we havent covered stuff like chi-squares so im not allowed to do that. thanks
OMG that's a BAD typo
you mean intersection and not union here.
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..........
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
It then follows that too.
You only need show that 2 of these 3 are equal
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.