That these events are independent?

[brendan]

I was wondering, if you are told that for two events A and B, We Have P(A)=0.4 and $P(A\mid B) = 0.4$\\
Can you assume as P(A) = P(A\mid B) That these events are independent?
regards
Brendan

 

[brendan]

Sorry guys,

That was Latex fonts

It should be
IF P(A) = 0.4 and P(A|B) = 0.4 can we assume that events A and B are independent?

regards
Brendan

 

[yyat]

Yes. To show this use

A, B are independent if and only if $$P(A\cap B)=P(A)P(B)$$,

$$P(A|B)P(B)=P(A\cap B)$$.