The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is $\frac{1}{4}$.The probability of selecting a blue ball at random from the same jar $\frac{1}{3}$.If the jar contains 10 orange balls, find the total number of ball

Given: The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls $=\frac{1}{4}$.The probability of selecting a blue ball at random from the same jar $=\frac{1}{3}$.The jar contains 10 orange balls.

To do: To find the total number of balls in the jar.

Solution:

Here the jar contains red, blue and orange balls.

Let the number of red balls be x.

Let the number of blue balls be y.

Number of orange balls $= 10$

Total number of balls $= x + y + 10$

Now, let P be the probability of drawing a ball from the jar

probability for a red ball$=\frac{x}{x+y+10}$

$\Rightarrow \frac{x}{x+y+10} =\frac{1}{4}$

$\Rightarrow 4x=x+y+10$

$\Rightarrow 3x-y=10\ \ \ \ ......................\left( 1\right)$

Probability for a blue ball$=\frac{y}{x+y+10}$

$\frac{1}{3} =\frac{y}{x+y+10}$

$x+y+10=3y$

$2y-x=10...............\left( 2\right)$

Multiplying eq. $( 1)$ by 2 and adding to eq. $( 2)$, we get,

$6x-2y+2y-x=20+10$

$5x=30$

$x=\frac{30}{5}$

$x=6$

Subs. $x = 6$ in eq. $( 1)$,

we get $y = 8$

Total number of balls $= x + y + 10 = 6 + 8 + 10 = 24$

Hence, total number of balls in the jar is 24.

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