# Ex.15.1 Q8 Probability Solution - NCERT Maths Class 10

## 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 ball drawn is

(i) red? (ii) not red?

## Text Solution

**What is known?**

A bag contains \(3\) red balls and \(5\) black balls. A ball is drawn at random from the bag.

**What is unknown?**

The probability that the ball drawn is (i) red ? (ii) not red.

**Reasoning:**

This question can be solved easily in two steps;

(i) First find out the probability of drawing the red ball by using the formula:

\[\begin{align}\text{Probability of an event}=\frac{\text { Number of possible outcomes }}{\text { Total no of favorable outcomes }}\end{align}\]

(ii) Then by using the formula of sum of complementary event find out the probability of not getting a red ball i.e. \(P(\text{R})=1-\text{P}(\text{ not E})=1-\frac{3}{8}=\frac{5}{8}\)

**Steps:**

No of red balls in a bag \(=3\)

No of black balls in a bag \(=5\)

\[\begin{align} \text{Total no of balls} &={3+5} \\ &=8 \end{align}\]

(i) Probability of drawing red ball =\(\begin{align}\frac{3}{8}\end{align}\)

(ii) Probability of not getting red ball

\[\begin{align} P({R})&=1-{P}(\text { not } {E}) \\&=1-\frac{3}{8} \\ &=\frac{5}{8} \end{align}\]