How to find the probability of an event "B" when given the probability of event A and the probability of the union of A and B?

Question

If P(A U B) = 0.4 and P(A) = 0.3, find P(B) if A and B are independent.

Answer 1

Hint:

Inclusion-exclusion (which is always true) implies that $$P(A\cup B) = P(A)+P(B)-P(A\cap B)$$

If we were to assume that $A$ and $B$ are independent, that would imply (and be true if and only if) that $$P(A\cap B) = P(A)\cdot P(B)$$

So, $0.4 = 0.3 + P(B) - 0.3\cdot P(B)$. Solve for $P(B)$.