The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is $\frac{1}{4}$. The probability of selecting a white marble at random from the same jar is $\frac{1}{3}$. If this jar contains 10 yellow marbles. What is the total number of marbles in the jar?

Given:

The probability of selecting a green marble at random from a jar that contains only green, white and yellow marbles is $\frac{1}{4}$.

The probability of selecting a white marble at random from the same jar is $\frac{1}{3}$.

The jar contains 10 yellow marbles.

To do:

We have to find the total number of marbles in the jar.

Solution:

Let the total number of marbles be $n$.

Probability of selecting a green marble $=\frac{1}{4}$

Probability of selecting a white marble $=\frac{1}{3}$

This implies,

Number of green marbles $=\frac{n}{4}$.

Number of white marbles $=\frac{n}{3}$.

Number of yellow marbles $=n-(\frac{n}{4}+\frac{n}{3})$

$=n-\frac{3 n+4 n}{12}$

$=\frac{12 n-7 n}{12}$

$=\frac{5 n}{12}$

Therefore,

$\frac{5 n}{12}=10$

$\Rightarrow n=2\times12=24$

The total number of marbles in the jar is $24$.

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