Question

A jar contains 24 marbles. Some of these are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is $\frac{2}{3}$. Find the number of blue marbles in the jar.

Answer 1

Total number of marbles = 24.
Let the number of blue marbles be x.
Then, the number of green marbles = 24 − x

∴ P(getting a green marble) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{24-x}{24}$

But, P(getting a green marble) = $\frac{2}{3}$ (given)

$$\begin{gathered} \therefore \frac{24-x}{24}=\frac{2}{3} \\ \Rightarrow 3(24-x)=48 \\ \Rightarrow 72-3x=48 \\ \Rightarrow 3x=72-48 \\ \Rightarrow 3x=24 \\ \Rightarrow x=8 \end{gathered}$$

Thus, the number of blue marbles in the jar is 8.