Question

A bag contains $3$ red balls and $5$ black balls . A ball is drawn at random from the bag . What is the probability that the drawn ball is

(1) red

(2) not red

Answer 1

Step 1: Find the probability that the drawn ball is red.

Given : Number of red balls $=3$

Number of black balls $=5$

Total number of balls $=3+5=8$

We know that Probability $=\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$

So, Probability of getting a red ball $=\frac{\text{no. of red balls}}{\text{total number of balls}}$

$=\frac{3}{8}$

Step 2 : Find the probability that the drawn ball is not red.

Now, number of balls which are not red $=$Number of black balls

$=5$

So, Probability of getting non red ball $=\frac{\text{no. of black balls}}{\text{total number of balls}}$

$=\frac{5}{8}$

Hence, the probability that the drawn ball is red is $\frac{3}{8}$and the probability that the drawn ball is not red is $\frac{5}{8}$