# Math Help - Events A,B (independent, mutually exclusive), Help!

1. ## Events A,B (independent, mutually exclusive), Help!

P(A/B)=0.2 , P(A/B^)=0.3 and P(B)=0.8

a) Are the events A, B independent ?
b) Are the events A, B mutually exclusive ?

Can someone solve this exercise please ?

2. I think it can be solved, here are some hints.

Events A and B are independant if $\displaystyle P(A\cap B) = P(A)\times P(B) , P(A/B) = P(A) , P(B/A) = P(B)$

Events A and B are mutually exclusive if $\displaystyle P(A\cap B) = 0$

Now with the information given $\displaystyle P(A/B) = \frac{P(A\cap B)}{P(B)} \implies 0.2 = \frac{P(A\cap B)}{0.8}\implies 0.16 = P(A\cap B)$

3. IF A and B are independent then

$P(A|B)=P(A)=P(A|B')$ which doesn't hold.