Question

Suppose you have a bag containing 30 marbles. If the probability of drawing a black marble is twice as likely not drawing a black marble, how many black marbles are in the bag?

Answer 1

The ratio of black marbles to non-black marbles is 2:1 which means that for every 1 marble which isn't black, there are two which are.

Answer 2

Let b be the number of black marbles
$$
P(\text{black})=2\times P(\text{not black})=\cfrac{\text{# black marbles}}{\text{total # of marbles}}=\cfrac{b}{30}\\
P(\text{not black})=\cfrac{30-b}{30}
$$
So now just solve for b:
$$
\cfrac{b}{30}=2\times\cfrac{30-b}{30}
$$

That's it!