If you try to fill in the Venn diagram, you can't put non-zero entries inside regions other than represented by pairwise intersections. They'll form up the sample space by themselves, which means $$P(E)=P(E\cap F)+P(E\cap G)=2/3$$

If you try to fill in the Venn diagram, you can't put non-zero entries inside regions other than represented by pairwise intersections. They'll form up the sample space by themselves, which means $$\mathbb P(E)=\mathbb P(E\cap F)+\mathbb P(E\cap G)=2/3$$