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By Ankit Gupta
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Updated on 11 Jun 2025, 18:18 IST
Mathematics is a subject that helps us understand the world around us by analyzing patterns and relationships. In Class 7, one important chapter you’ll come across is Chapter 25, titled "Data Handling IV (Probability)." This chapter is all about probability, a branch of mathematics that helps us determine the likelihood of an event happening.
Probability is something we experience every day, whether it’s predicting the weather, guessing the outcome of a coin toss, or even figuring out the chances of winning a game. In this chapter, you will learn how to calculate the probability of various events based on the data provided. This chapter is a continuation of your learning from earlier chapters on data handling and introduces you to a more specific and interesting concept—probability.
In simple terms, probability is the chance or likelihood that a particular event will happen. The probability of an event ranges from 0 to 1. If the probability is 0, it means the event will never happen. If the probability is 1, it means the event will definitely happen. Understanding probability allows us to make informed predictions and decisions in situations involving uncertainty.
Do Check: RD Sharma Solutions for Class 7 Maths
The chapter begins with a brief overview of how to calculate probability. You will be introduced to the formula for probability, which is the ratio of the number of favorable outcomes to the total number of possible outcomes. Through examples and practice problems, you will understand how to apply this formula to real-life situations, such as rolling a die or picking a colored ball from a bag.
The RD Sharma Solutions for Class 7 Maths Chapter 25 are designed to help you grasp these concepts easily. They provide step-by-step explanations of each question, breaking down complex problems into simpler ones. The solutions guide you through every calculation and help you understand the logic behind the steps. With clear explanations and practical examples, you’ll gain confidence in solving probability-related problems.
This chapter not only strengthens your understanding of data handling but also prepares you for more advanced topics in higher classes. By practicing these problems, you’ll develop critical thinking skills and the ability to analyze situations based on probability. So, get ready to explore the exciting world of probability and sharpen your math skills with the RD Sharma solutions.
RD Sharma Class 7 Chapter 25 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 25 PDF.
In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.
Q1. A coin is tossed 1000 times with the following frequencies:
Head: 445, Tail: 555
When a coin is tossed at random, what is the probability of getting:
(i) A head?
(ii) A tail?
Solution:
Given total number of times a coin is tossed = 1000
Number of times a head comes up = 445
Number of times a tail comes up = 555
(i) Probability of getting head = number of heads / total number of trials
= 445 / 1000
= 0.445
(ii) Probability of getting tail = number of tails / total number of trials
= 555 / 1000
= 0.555
Q2. A die is thrown 100 times, and outcomes are noted as given below:
| Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 21 | 9 | 14 | 23 | 18 | 15 |
If a die is thrown at random, find the probability of getting a/an:
(i) 3
(ii) 5
(iii) 4
(iv) Even number
(v) Odd number
(vi) Number less than 3.
Solution:
Given total number of trials = 100
(i) From the table, number of times 3 comes up = 14
Probability of getting 3 = frequency of 3 / total number of trials
= 14 / 100
= 7 / 50
(ii) From the table, number of times 5 comes up = 18
Probability of getting 5 = frequency of 5 / total number of trials
= 18 / 100
= 9 / 50
(iii) From the table, number of times 4 comes up = 23
Probability of getting 4 = frequency of 4 / total number of trials
= 23 / 100
(iv) Frequency of getting an even number = Frequency of 2 + Frequency of 4 + Frequency of 6
= 9 + 23 + 15
= 47
Probability of getting an even number = frequency of an even number / total number of trials
= 47 / 100
(v) Frequency of getting an odd number = Frequency of 1 + Frequency of 3 + Frequency of 5
= 21 + 14 + 18
= 53
Probability of getting an odd number = frequency of odd number / total number of trials
= 53 / 100
(vi) Frequency of getting a number less than 3 = Frequency of 1 + Frequency of 2
= 21 + 9
= 30
Probability of getting a number less than 3 = frequency of number less than 3 / total number of trials
= 30 / 100
= 3 / 10
Q3. A box contains two pairs of socks of two colours (black and white). I have picked out a white sock. I pick out one more with my eyes closed. What is the probability that I will make a pair?
Solution:
Given number of socks in the box = 4
Let B and W denote black and white socks respectively. Then we have
S = {B, B, W, W}
If a white sock is picked out, then the total number of socks left in the box = 3
Number of white socks left = 2 – 1 = 1
Probability of getting white socks = number of white socks left in the box / total number of socks left in the box
= 1 / 3
Q4. Two coins are tossed simultaneously 500 times and the outcomes are noted as given below:
| Outcome | Two heads (HH) | One head (HT or TH) | No head (TT) |
| Frequency | 105 | 275 | 120 |
If the same pair of coins is tossed at random, find the probability of getting:
(i) Two heads
(ii) One head
(iii) No head.
Solution:
Given number of trials = 500
(i) Probability of getting two heads = frequency of getting 2 heads / total number of trials
= 105 / 500
= 21 / 100
(ii) Probability of getting one head = frequency of getting 1 head / total number of trials
= 275 / 500
= 11 / 20
(iii) Probability of getting no head = frequency of getting no heads / total number of trials
= 120 / 500
= 6 / 25
Probability in this chapter refers to the likelihood or chance of an event happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This concept helps in predicting the chances of events like tossing a coin or drawing a card from a deck.
To calculate probability, you use the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
For example, if you roll a fair die, the probability of getting a 3 is 1/6 because there is one favorable outcome (rolling a 3) and six possible outcomes (1, 2, 3, 4, 5, 6).
Favorable outcomes are the outcomes that satisfy the condition we are interested in. For example, if the question asks for the probability of rolling an even number on a die, the favorable outcomes would be 2, 4, and 6, as they are the even numbers on a standard die.
Yes! RD Sharma Solutions for Class 7 Maths Chapter 25 provide step-by-step explanations for each problem. These solutions break down the problems into simpler steps, making it easier to understand the logic behind each calculation and the use of probability formulas.
Practicing probability problems is important because it helps reinforce the concept and improves problem-solving skills. The more problems you solve, the better you’ll understand how to calculate probabilities in different situations. It also boosts your confidence for exams.
In Chapter 25, you can expect problems related to simple probability calculations, such as finding the probability of specific outcomes in events like rolling a die, drawing a card, or selecting an object from a set. The problems also include examples involving the calculation of favorable and total outcomes.