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.
Solution:
Total number of marbles = 24.
Let the number of blue marbles be x.
Then, the number of green marbles = 24 − x
$\therefore \mathrm{P}$ (getting a green marble) $=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{24-x}{24}$
But, $P$ (getting a green marble) $=\frac{2}{3}$ (given)
$\therefore \frac{24-x}{24}=\frac{2}{3}$
$\Rightarrow 3(24-x)=48$
$\Rightarrow 72-3 x=48$
$\Rightarrow 3 x=72-48$
$\Rightarrow 3 x=24$
$\Rightarrow x=8$
Thus, the number of blue marbles in the jar is 8.