Question

The probability of selecting a white ball at random from a container that contains only white, yellow and red balls is 1/7. The probability of selecting a yellow ball at random from the same container is 1/5. If the container contains 23 red balls, find the total number of balls in the container.

Answer 1

Let’s assume that there are ‘x’ number of balls in the container.
We know that the sum of all the elementary events is equal to one.
Here, the selection of white, yellow or red balls from the container are elementary events. So, P(White) + P(Yellow) + P(Red) = 1
P(White) + P(Yellow) + P(Red) = 1
(1/7) + (1/5) + P(Red) = 1
P(Red) = 1 - (1/7) - (1/5) = 23/35 … (i)
In the question, it is given that there are 23 Red balls in the container.
So, P(Red) = 23/x …. (ii)
eq (i) and (ii) are equal
Therefore, P(Red) = 23/35 = 23/x
So, x = 35

Total number of balls in the container is 35 balls.