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.
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