A jar contains 24 marbles, some 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 balls in the jar.

Given:

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

To do:

We have to find the number of blue balls in the jar.

Solution:

Total number of marbles $=24$

Let the number of green marbles be $x$.

This implies,

The number of blue marbles $=24-x$

The total number of possible outcomes $n=24$.

Total number of favourable outcomes(getting a green marble) $=x$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability of getting a green marble $=\frac{x}{24}$

According to the question,

$\frac{x}{24}=\frac{2}{3}$

$ \frac{x}{8}=2$

$x=2(8)$

$x=16$

This implies,

The number of blue balls in the jar $=24-16=8$

Therefore, the number of blue balls in the jar is 8.