# 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:

Probability of an event

\[=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }\]

(ii) Then by using the formula of sum of complementary event find out the probability of not getting a red ball i.e.

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

**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

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