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.

Answer 1

We know,
P(getting red ball) = 1/4
P(getting blue ball) = 1/3
Let the no. of balls = x 
Therefore, P(getting orange ball) = 10/x

We know,
P(getting red ball) + P(getting blue ball) + P(getting orange ball) = 1
⇒1/4 + 1/3 + 10/x = 1
⇒10/x = 1 -1/4 -1/3
⇒10/x = 1 - 7/12
⇒10/x = 5/12
⇒10 * 12 = 5 * x
⇒x = 24

Therefore, the no. of balls = x 
                                          = 24

Answer 2

the question is to find the total number of balls in the bag.

the total number of balls is equal to number of red balls + blue + Orange balls .

probability of getting a red ball is 1/4

probability of selecting a blue ball is 1/3

the number of orange balls is 10.

so , 10 + r + b is equal to x .

10 /x = 1 - 1/4 - 1/3

10/ x = 5 / 12

120 = 5y

=> *y = 24*