Find P(A) from the following information...

Question

Let,

P(B and Complement of A)=0.1 P(B)=0.3 P(A and Complement of B)=0.2

The value of P(A) is closest to:

(a) 0.1 (b) 0.2 (c) 0.3 (d) 0.4 (e) 0.5

I've tried to solve this question many different ways, and just can't find a way

Answer 1

If there is only events $A$ and $B$, you can solve by thinking graphically.
$P(B \cap A')$: means all the area of $B$ not inside $A$.
$P(B)$ : The total area of $B$

So $P(B) - P(B \cap A') = 0.3 - 0.1 = 0.2 $ This is the area of intersection of $B$ and $A$.

So: $P(A) = 0.2 + P(A \cap B') = 0.2 + 0.2 = 0.4$