# Math Help - independant events, probability

1. ## independant events, probability

Events A and B are independent.
Given also that
P(A) = 3/4 and P(A ∩ B ′ ) = 1/4

Find
(a) P(A ∩ B),
(b) P(B),
(c) P(A′ ∩ B ′ ).
can someone please explain in this question If events and A and B are independent of each other, than why is it that the p (A ∩ B ′) = 1/4?
Is that not the probability that event 'A' happens and 'B' does not , should it not also equal 3/4 ? As my understanding is if both events are independent of each other than the probability of 'A' happening is the same weather or not 'B' has happened.

Thanks.

2. If events $E~\&~F$ are independent then that tell you $P(E \cap F) = P(E)P(F)$.
Each of these pairs is independent: $E~\&~{F'}$, ${E'}~\&~F$, ${E'}~\&~{F'}$.

So you know that $\frac{1}{4} = P(A \cap B') = P(A)P(B')$.