# Math Help - mutually exclusive problem

1. ## mutually exclusive problem

Hi I'm having trouble with this question:

Let A and B be independent events, where P(A) = 0 and P(B)=x
a) write down an expression for P(A ∩ B)
b) Given that P(A U B) = 0.8,
i)find x
ii) find P(A ∩ B)
c) Hence, explain why A and B are not mutually exclusive

Any help is greatly appreciated. =)

2. Originally Posted by adsfdgfh
Hi I'm having trouble with this question:

Let A and B be independent events, where P(A) = 0 and P(B)=x
a) write down an expression for P(A ∩ B)
b) Given that P(A U B) = 0.8,
i)find x
ii) find P(A ∩ B)
c) Hence, explain why A and B are not mutually exclusive

Any help is greatly appreciated. =)
Substitute what you're given into the usual formula $\Pr(A \cup B) = \Pr(A) + \Pr(B) - \Pr(A \cap B)$ and solve for $\Pr(A \cap B)$.

3. i've done that and got P(A∩B) = 0 which would mean they ARE mutually exclusively. Im pretty sure i did something wrong but can't seem to find it.

4. Originally Posted by adsfdgfh
i've done that and got P(A∩B) = 0 which would mean they ARE mutually exclusively. Im pretty sure i did something wrong but can't seem to find it.
If P(A) = 0 (which is what you have stated in your first post) then obviously P(A∩B) = 0 ....

But if P(A) = 0 I wouldn't have thought that discussing the mutual exclusivity of A and B made much sense ....

5. Originally Posted by mr fantastic
If P(A) = 0 (which is what you have stated in your first post) then obviously P(A∩B) = 0 ....

But if P(A) = 0 I wouldn't have thought that discussing the mutual exclusivity of A and B made much sense ....
sorry, i just found out there was actually a typo in the assignment. P(A) is actually 0.6, which makes the question a lot easier to do
thanks for all your help though