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?

   

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 

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