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

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## 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?

Video Solution
Probability
Ex 15.1 | Question 8

## 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}

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