#### Question

The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar 1/3. If the jar contains 10 orange balls, 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

P(a red ball) =x/(x+x+10)

1/4=x/(x+x+10)

4x=x+x+10

3x-y=10.........(i)

Next

P(a blueball) =y/(x+x+10)

1/3=y/(x+x+10)

3y=x+x+10

2y-x=10 ......(ii)

Multiplying eq. (i) by 2 and adding to eq. (ii), we get

6x - 2y = 20

`-x + 2y = 10`

5x = 30

x=6

Subs. x = 6 in eq. (i), 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.