Question

A bag contains 5 red balls and some blue balls. if the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

Answer 1

Hint: In this question, you are provided with a relation between the probability of red balls and the probability of blue balls. Assume the number of blue balls to be x and then find the probability of blue and red balls by using formula $\dfrac{{No.{\text{ }}of{\text{ }}favourable{\text{ }}outcomes}}{{Total{\text{ }}No.{\text{ }}of{\text{ }}outcomes}}$
After that use, the relation is given in the question i.e. Probability of blue balls = 2$\times$Probability of red balls, and find the value of x.

Complete step-by-step answer:
Let us assume the number of blue balls in the bag to be x.
So according to question total number of balls in the bag = x+5
So probability of drawing a blue ball from the bag = $\dfrac{{No.{\text{ }}of{\text{ }}favourable{\text{ }}outcomes}}{{Total{\text{ }}No.{\text{ }}of{\text{ }}outcomes}}$= $\dfrac{x}{{5 + x}}$
Probability of drawing a red ball from the bag = $\dfrac{{No.{\text{ }}of{\text{ }}favourable{\text{ }}outcomes}}{{Total{\text{ }}No.{\text{ }}of{\text{ }}outcomes}}$= $\dfrac{5}{{5 + x}}$
Now, it is given in the question that P(B) = 2P(R)
so, $\dfrac{x}{{5 + x}}$=2($\dfrac{5}{{5 + x}}$)
On multiplying x+5 on both sides, we get x = 10.
Thus, the number of blue balls in the bag is equal to 10.

Note: The quality or state of being likely or the extent to which something may or may not happen is known as probability. The simplest example to explain probability is that of a coin flip whenever a coin is flipped it can either turn up as a head or a tail thus the probability of getting a head or a tail is 50% or $\dfrac{1}{2}$.