The formula that $P(A\vee B)= P(A) + P(B)$ is only true if events $A$ and $B$ are disjoint. In this case, simply adding $P(A)$ and $P(B)$ double counts the case where both $A$ and $B$ occur.
The correct formula in this case would be $P(A\vee B)= P(A) + P(B) - P(A\wedge B)$, which should give you the correct answer. Note that if $A$ and $B$ are indeed disjoint, $P(A\wedge B)$ is $0$ by definition, so we can see that the first formula is just a subcase of the more general formula.
EDIT: I respond to your comment to the other answer, which suggests that it is not completely clear to you what the difference between “independent” and “disjoint” is.
Independence, intuitively, means that the outcome of one event does not affect the outcome of the other. Formally, if A and B are independent, $P(A|B)=P(A)$ and $P(B|A)= P(B)$. Notably, this allows us to conclude the familiar multiplication rule for independent events: if A and B are independent, $P(A\wedge B)= P(A)\cdot P(B)$. To give an example, suppose that tommorow may be sunny or rainy. Also, you might win the lottery next week. These events are independent— the outcome of one will not influence the other.
On the other hand, disjoint events are events which cannot occur at the same time. In other words, if A and B are disjoint, then either A is true or B is true, (or maybe neither!), but it is not possible that both are true. Suppose that you are picking a single marble out of a bag with red and blue marbles. You might pick a red marble or you might pick a blue marble, but you can’t pick a blue marble and a red marble at the same time. Hence the events “pick a red marble” and “pick a blue marble” are disjoint.
Therefore, not only are the two ideas very different, but in fact disjoint events are never independent. This is because, for disjoint events, if A is occurs, then we know that B cannot occur. So the outcome of A can allow us to make a conclusion about the outcome of B.