Probability of Marbles in Bag

A bag contains a combination of red, blue, and green marbles. The total number of marbles in the bag is 30. If the probability of drawing a blue marble is $\frac{1}{6}$, and the probability of drawing a red marble is $\frac{1}{3}$, how many green marbles are there in the bag?

Let the number of blue marbles be denoted as $B$, the number of red marbles as $R$, and the number of green marbles as $G$. We know from the problem:

1. Total marbles: $$R + B + G = 30$$

2. Probability of blue marbles: $$P(B) =\frac{B}{30} =\frac{1}{6}$$

3. Probability of red marbles: $$P(R) =\frac{R}{30} =\frac{1}{3}$$

Using these probabilities, you can find the exact number of each color of marble.