Probability Class 10 Notes
Get ready to increase your Maths board exam score with Vedantu’s probability class 10 notes. You can use the expert solutions given at Vedantu in order to learn how you would find the number of colored balls in a bag and much more? Or after understanding the concept of probability, you can also prove that a given event will be an impossible event.
So, let us understand how to use the probability formula with which you can find answers based on the information about the number of favorable outcomes along with the total number of outcomes.
NCERT Class 10 Probability Revision Notes At Vedantu
Revise your probability concepts to improve your exam score with our NCERT class 10 probability topic notes and other resources.
Probability Class 10 Important Questions PDF
This PDF on Probability Problems for Class 10 CBSE is created as per the latest syllabus. Here in the following downloadable PDF, we have covered everything related to Probability Class 10. Also, there are solved step-by-step examples which you can have a look at for your better understanding. So, with our probability class 10 important questions PDF, you can have a clear idea of the topic and should be able to get high marks in Class 10 Mathematics CBSE Board exams.
Formula for Solving Probability Problems for Class 10 CBSE
In the general formula of probability:
P(A) means 'the probability of A' where A is an event we are interested in,
P(A|B) stands for 'the probability of A given that B occurs', and
P( A0) stands for 'the probability of A0 ', or it tells about 'the probability that A does not take place.’
The Rules Of Probability
Probability has its own set of rules that are used in solving both simple and complex probability problems. So, here are three most widely used rules of probability.
Rule 1: The Addition rule
Rule 2: The Multiplication rule
Rule 3: The Complement rule
1. The Addition Rule
The representation for this rule is as follows:
P(A or B) = P(A) + P(B) - P(A and B)
If there are two events A and B which are mutually exclusive of each other or the two events which can’t take place together, then the third term is 0. That means, the rule can then be reduced to:
P(A or B) = P(A) + P(B)
2. The Multiplication Rule
The formula for this rule is:
P(A and B) = P(B) * P(A | B) or P(A) * P(B|A)
In this rule, both the events A and B are independent events. The formula can also be reduced to P(A and B) = P(A) * P(B). However, this rule states that each event out of these 2 events is not affected by the outcome of the other event.
Consider the coin toss. If the first result came as a head then also there is no guarantee that in the next toss the result will be tails. So, the probability is 0.25 or 25% that it can be heads again or tails. Are you wondering how it's 25%? Let's have a look at the calculations.
P = P(heads) * P(tails) = (0.5) * (0.5) = 0.25
3. The Complement Rule
Here is its representation…
P(not A) = 1 - P(A)
Here, the two events, A and B can never take place together but one event out of these two will always take place. For instance, if the weatherman says that there’s a 40% chance of rain tomorrow then the chances of no rain are
40% = 0.4
P(no rain) = 1 - P(rain) = 1 - 0.4 = 0.6/ 60%.
FAQs on Probability For Class 10
1. What is the probability formula for calculating the chance of an event in Class 10 CBSE Maths?
The probability of an event is calculated using the formula P(E) = Number of favourable outcomes / Total number of possible outcomes. This formula is used to determine how likely a particular event is to occur within a defined set of possibilities.
2. Which rules of probability should Class 10 students know for board exams?
There are three main rules that students should understand:
- Addition Rule: For mutually exclusive events, P(A or B) = P(A) + P(B).
- Multiplication Rule: For independent events, P(A and B) = P(A) × P(B).
- Complement Rule: The probability of an event not occurring is P(not A) = 1 - P(A).
3. How can you quickly identify if an event is impossible, certain, or has intermediate probability?
An impossible event has a probability of 0; a certain event has a probability of 1. Any value between 0 and 1 shows an event has some chance of occurring. For example, P = 0.5 means a 50% chance.
4. Why is probability important for real-life decision making as per Class 10 syllabus?
Probability helps you assess risks and chances in daily life, like predicting weather, playing games, or making business choices. Understanding probability enables logical thinking and improves reasoned decisions in uncertain situations.
5. What kind of questions on probability typically appear in Class 10 board exams?
Typically, questions cover:
- Finding probability of simple events (like drawing a red ball)
- Calculating probability using coins or dice
- Applying rules (addition, multiplication, complement)
- Proving whether an event is impossible or certain
6. How do you differentiate between equally likely and mutually exclusive events in the context of probability?
Equally likely events have the same probability of happening (e.g., all faces on a fair die). Mutually exclusive events cannot both occur at the same time (e.g., getting a head or a tail in a single coin toss). Understanding this difference is important for applying the correct probability rule in exams.
7. What misconceptions should students avoid when answering probability questions in exams?
Common misconceptions include:
- Assuming all events are equally likely without checking the sample space
- Confusing independent events with dependent ones
- Forgetting to subtract overlapping outcomes in the addition rule
- Not verifying if events are mutually exclusive before applying formulas
Being aware of these helps avoid common mistakes in board questions.
8. If a question asks for the probability of 'at least one' event happening, how should it be solved?
Such questions are often simplified using the complement rule: Probability of at least one = 1 - Probability of none. This approach makes complicated calculations easier, especially for problems involving multiple trials, and is encouraged in board exams for clarity and correctness.
9. How should students justify their steps for full marks in probability questions during the 2025-26 CBSE exams?
Each solution should include:
- Explicitly stating assumptions (like all outcomes are equally likely)
- Writing the total number of possible outcomes
- Clearly listing favorable outcomes
- Using the correct formula
- Providing a direct, labeled answer (like 'Thus, probability = 3/6 = 0.5')
10. What real-life scenario can be used as an example to explain probability to a Class 10 student?
A simple scenario is tossing a coin to decide who goes first in a game. The probability of getting heads is 1 out of 2 possible outcomes, i.e., 0.5 or 50%. Such real-world examples help make the concept easier to grasp and apply in everyday decisions.
