Question

A bag contains white, black and red balls only. A ball is drawn at random

from the bag. If the probability of getting a white ball is 3

10

and that of a

blackball is 2

5

, then find the probability of getting a red ball. If the bag

contains 20 black balls, then find the total number of balls in the bag.​

Answer 1

Probability of getting a red ball = $\frac{3}{10}$

Total number of balls in the bag = 50

Step-by-step explanation:

We are given that a bag contains white, black and red balls only.

A ball is drawn at random   from the bag. The probability of getting a white ball is  $\frac{3}{10}$  and that of a  blackball is  $\frac{2}{5}$ .

Since, we know that the sum of all cases of probabilities is equal to 1, that means;

There are only three types of balls in the bag : white, black and red. So, the sum of probabilities of getting each ball individually must be equal to 1.

(a) So, Probability of getting a white ball + Probability of getting a black ball + Probability of getting a red ball  =  1

      ⇒  $\frac{3}{10}+\frac{2}{5}+\text{Probability of getting a red ball} =1$

      ⇒  Probability of getting a red ball  =  $1-\frac{3}{10}-\frac{2}{5}$

                                                                 =  $1-\frac{3}{10}-\frac{4}{10}$

                                                                 =  $1-\frac{7}{10}$

                                                                 =  $\frac{3}{10}$

Hence, the probability of getting a red ball is  $\frac{3}{10}$ .

(b) Now, we are given that there are 20 black balls in the bag and we have to find the total number of balls in the bag.

As we know that  Probability of any event  =  $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

So,  Probability of getting a black ball  =  $\frac{\text{Number of black balls in the bag}}{\text{Total number of balls in the bag}}$

                            $\frac{2}{5}= \frac{20}{\text{Total number of balls in the bag}}$

      $\text{Total number of balls in the bag} =\frac{20\times 5}{2}$

                                                          =  $\frac{100}{2}=50$

Therefore, there are 50 balls in the bag.