RD Sharma Solutions Class 9 Chapter 25 are given here which consist of questions and answers related to Probability. “Probability is a measure of the possibility that an event will occur”. It is qualified as a number between zero and one. A simple example of probability is tossing of the coin. A coin consists of two sides, head and a tail, which means there are only two outcomes. The probability of tails equals the probability of heads. The probability of tails or heads is 1/2 since there are no other outcomes.

What is Probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur, how likely they are to happen, using probability. Practice more Maths concepts with RD Sharma Class 9 Solutions and score good marks in exams.

## Download PDF of RD Sharma Solutions for Class 9 Maths Chapter 25 Probability

### Access Answers to Maths RD Sharma Chapter 25 Probability

__Exercise 25.1 Page No: 25.13__

**Question 1: A coin is tossed 1000 times with the following sequence: **

**Head: 455, Tail: 545**

**Compute the probability of each event.**

**Solution: **

Coin is tossed 1000 times, which means, number of trials are 1000.

Let us consider, event of getting head and event of getting tail be E and F respectively.

Number of favorable outcome = Number of trials in which the E happens = 455

So, Probability of E = (Number of favorable outcome) / (Total number of trials)

P(E) = 455/1000 = 0.455

Similarly,

Number of favorable outcome = Number of trials in which the F happens = 545

Probability of the event getting a tail, P(F) = 545/1000 = 0.545

**Question 2: Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:**

**Two heads: 95 times**

**One tail: 290 times**

**No head : 115 times**

**Find the probability of occurrence of each of these events.**

**Solution: **

We know that, Probability of any event = (Number of favorable outcome) / (Total number of trials)

Total number of trials = 95 + 290 + 115 = 500

Now,

P(Getting two heads) = 95/500 = 0.19

P(Getting one tail) = 290/500 = 0.58

P(Getting no head) = 115/500 = 0.23

**Question 3: Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:**

Outcome |
No head |
One head |
Two heads |
Three heads |

Frequency |
14 |
38 |
36 |
12 |

**If the three coins are simultaneously tossed again, compute the probability of:**

**(i) 2 heads coming up**

**(ii) 3 heads coming up**

**(iii) At least one head coming up**

**(iv) Getting more heads than tails**

**(v) Getting more tails than heads**

**Solution:**

We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)

In this case, total numbers of outcomes = 100.

**(i)** Probability of 2 Heads coming up = 36/100 = 0.36

**(ii)** Probability of 3 Heads coming up = 12/100 = 0.12

**(iii)** Probability of at least one head coming up = (38+36+12) / 100 = 86/100 = 0.86

**(iv)** Probability of getting more Heads than Tails = (36+12)/100 = 48/100 = 0.48

**(v)** Probability of getting more tails than heads = (14+38) / 100 = 52/100 = 0.52

**Question 4: 1500 families with 2 children were selected randomly, and the following data were recorded:**

**If a family is chosen at random, compute the probability that it has:**

**(i) No girl (ii) 1 girl (iii) 2 girls (iv) At most one girl (v) More girls than boys**

**Solution: **

We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)

In this case, total numbers of outcomes = 211 + 814 + 475 = 1500.

(Here, total numbers of outcomes = total number of families)

**(i)** Probability of having no girl = 211/1500 = 0.1406

**(ii)** Probability of having 1 girl = 814/1500 = 0.5426

**(iii)** Probability of having 2 girls = 475/1500 = 0.3166

**(iv)** Probability of having at the most one girl = (211+814) /1500 = 1025/1500 = 0.6833

**(v)** Probability of having more girls than boys = 475/1500 = 0.31

**Question 5: In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that on a ball played:**

**(i) He hits boundary (ii) He does not hit a boundary.**

** Solution:**

Total number of balls played by a player = 30

Number of times he hits a boundary = 6

Number of times he does not hit a boundary = 30 – 6 = 24

We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)

Now,

**(i)** Probability (he hits boundary) = (Number of times he hit a boundary) / (Total number of balls he played)

= 6/30 = 1/5

**(ii)** Probability that the batsman does not hit a boundary = 24/30 = 4/5

**Question 6: The percentage of marks obtained by a student in monthly unit tests are given below:**

**Find the probability that the student gets**

**(i) More than 70% marks**

**(ii) Less than 70% marks**

**(iii) A distinction**

** Solution:**

Total number of unit tests taken = 5

We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)

**(i)** Number of times student got more than 70% = 3

Probability (Getting more than 70%) = 3/5 = 0.6

**(ii)** Number of times student got less than 70% = 2

Probability (Getting less than 70%) = 2/5 = 0.4

**(iii)** Number of times student got a distinction = 1

Probability (Getting a distinction) = 1/5 = 0.2

**Question 7: To know the opinion of the students about Mathematics, a survey of 200 students were conducted. The data was recorded in the following table:**

**Find the probability that student chosen at random:**

**(i) Likes Mathematics (ii) Does not like it.**

**Solution:**

Total number of students = 200

Students like mathematics = 135

Students dislike Mathematics = 65

We know, Probability of an event = (Number of Favorable outcomes) / (Total Numbers of outcomes)

(i) Probability (Student likes mathematics) = 135/200 = 0.675

(ii) Probability (Student does not like mathematics) = 65/200 = 0.325

__Exercise VSAQs Page No: 25.16__

**Question 1: Define a trial.**

**Solution: **When we perform an experiment it is called a trial of the experiment. Whereas, an operation which can produce some well-defined outcomes is called an experiment.

For example, we have 6 possible outcomes while rolling a die.

**Question 2: Define an elementary event.**

**Solution:** An outcome of a trial of an experiment is an elementary event.

**Question 3: Define an event.**

**Solution:** A subset of the sample space is called an event.

For Example: In the experiment of tossing a coin:

Event E = the event of getting a head

Event F = the event of getting a tail

**Question 4: Define Probability of an Event.**

**Solution:** Suppose an event E can happen in m ways out of a total of n possible equally likely ways.

Then, the probability of occurrence of the event = P(E) = m/n.

## RD Sharma Solutions for Chapter 25 Probability

In the 25th chapter of Class 9 RD Sharma Solutions students will study important concepts listed below:

- Probability Introduction
- Various approaches to Probability
- Experimental or empirical approach to Probability
- Some important terms: Trial, Elementary event and Compound event