Question

A bag contains $3$ red balls and $5$ black balls. A ball drawn at random from the bag What is the probability that the ball drawn is (i) red? (ii) not red?

Answer 1

Hint : To solve this question, we will start with finding the total number of balls in the bag, then for the first part we will take the favourable outcomes of getting red balls, and for the second part we will take the favourable outcomes of getting black balls, because black ball is equals to not red balls, then after applying the values in the probability formula, we will get our required answers.

Complete step-by-step answer :
We have been given that a bag contains $3$ red balls and $5$ black balls. It is given that a ball drawn at random from the bag, we need to find the probability that the ball drawn is (i) red (ii) not red.
So, total number of outcomes of balls $= {\text{ }}8$
The number of favourable outcomes of getting red balls $= {\text{ }}3$
And the number of favourable outcomes of getting black balls $= {\text{ }}5$
We know that, Probability $= \dfrac{{{\text{favourable outcomes}}}}{{{\text{total outcomes}}}}$
On applying the values in the above formula, we get
(i) Probability of getting a red ball $= \dfrac{3}{8}$
(ii) Probability of not getting a red ball $=$ Probability of getting a black ball
Probability of not getting a red ball $= \dfrac{5}{8}$
Thus, probability of getting a red ball is $\dfrac{3}{8}$ and probability of not getting a red ball is $\dfrac{5}{8}.$

Note : To solve the second part of the question, there is an alternate method of finding the probability of not getting a red ball.
Probability of not getting a red ball $= {\text{ }}1{\text{ }} -$probability of getting a red ball.
Probability of not getting a red ball $= 1 - \dfrac{3}{8}$
$= \dfrac{5}{8}$
Here, in the formula, we have subtracted from $1,$ because $1$ indicates certainty of the event.