Question

A bag contains 12 balls .Some are red and others are blue , the probability of drawing red balls is $\dfrac{1}{3}$ .Find the number of blue balls.

Answer 1

We are given the number of elements in the sample space that is 12 and with the probability of drawing the red ball we can equate it with $\dfrac{{n(A)}}{{n(S)}}$with which we can find the number of red balls and subtracting it from the total number of balls we get the number of blue balls.

Complete step by step solution:
We are given that the bag contains 12 balls
That is , $n(S) = 12$
Let A be the red balls
And let B be the blue balls
We are given the probability of drawing a red ball to be $\dfrac{1}{3}$
That is , $P(A) = \dfrac{1}{3}$…………..(1)
We know that $P(A) = \dfrac{{n(A)}}{{n(S)}}$……………(2)
Equating (1) and (2) we get
$\Rightarrow \dfrac{{n(A)}}{{n(S)}} = \dfrac{1}{3} \\\ \Rightarrow \dfrac{{n(A)}}{{12}} = \dfrac{1}{3} \\\ \Rightarrow n(A) = \dfrac{{12}}{3} = 4 \\\$
We get that the number of red balls is 4
Therefore , the number of blue balls = total number of balls – number of red balls
= 12 – 4
= 8
Hence the number of blue balls is 8.

Note:

1. A probability of 0 means that an event is impossible.
2. A probability of 1 means that an event is certain.
3. An event with a higher probability is more likely to occur.
4. Probabilities are always between 0 and 1.
5. The probabilities of our different outcomes must sum to 1.