CBSE Notes Class 10 Maths Chapter 14 Probability

CBSE Notes Class 10 Maths Chapter 14 – Probability help you understand the basic concepts of chance and likelihood in a simple and clear way. In this chapter, you will learn about theoretical probability, outcomes, events, and how to calculate the probability of different situations. These CBSE Notes provide important formulas, step-by-step explanations, and solved examples to make revision easy and help you prepare confidently for your Class 10 board exams.

1.0Download CBSE Notes for Class 10 Maths Chapter 14: Probability - Free PDF!!

Download your CBSE Notes for Class 10 Maths Chapter 14: Probability in free PDF format for quick and effective revision. These notes include clear explanations, key formulas, and solved examples to help you prepare confidently for your Class 10 board exams.

2.0CBSE Class 10 Maths Notes Chapter -14 Probability - Revision Notes

Important Concepts in Probability

1. Experiment: An experiment refers to an action or trial that leads to outcomes. For example, rolling a die.
2. Outcome: An outcome is a possible result of an experiment. For a die, the outcomes are 1, 2, 3, 4, 5, 6.
3. Sample Space: The sample space is the set of all possible outcomes of an experiment. For instance, in tossing a coin twice, the sample space is {HH, HT, TH, TT}.
4. Event: An event is a subset of the sample space. For example, getting an even number when rolling a die is an event {2, 4, 6}.

Types of Events:

• Simple Event: An event with a single outcome (e.g., rolling a 3 on a die).
• Compound Event: An event with more than one outcome (e.g., rolling an even number).

Definitions

• Probability: The probability of an event is the ratio of the number of favourable outcomes to the total number of outcomes in the sample space.
• Complementary Events: Events that are mutually exclusive and exhaustive. For example, if A is rolling a 6 on a die, the complement is not rolling a 6.

Formulas

Probability of an event $P(E)\text{. }$:

$P(E)=\text{ Number of favorable outcomes / Total number of outcomes }$

Probability of complementary events:

$P(\mathrm{Not}E)=1-P(E)$

Probability in case of equally likely outcomes

$P(E)=\text{ Number of outcomes in E / Total number of outcomes in Sample Space }$

Tips and Tricks

• Visualise the Problem: For compound experiments, make use of tree diagrams or tables so that results can be readily seen.
• Verify Total Probability: The probabilities of all possible events in a sample space always add up to 1.
• Simplify Compound Events: Break compound events into simple events to calculate probabilities step by step.

3.0CBSE Class 10 Maths Notes Chapter -14 Probability - Key Notes

Experiment : An action or operation which can produce some well-defined result is known as experiment.

Outcomes : The possible results of a random experiment are called outcomes.

Trial : When an experiment is repeated under similar conditions and it does not give the same result each time but may result in any one of the several possible outcomes is called a trial.

E.g., If a coin is tossed 100 times, then one toss of the coin is called a trial.

Event : The collection of all or some outcomes of a random experiment is called an event.

E.g., Suppose we toss a pair of coins simultaneously and let E be the event of getting exactly one head. Then, the event E contains HT and TH.

Elementary or Simple Event : An outcome of a trial is called an elementary event.

Note : An elementary event has only one element.

E.g., Let a pair of coins is tossed simultaneously. Then, possible outcomes of this experiment are–

• HH : Getting H on first and H on second (= E₁) [H = Head, T = Tail and E = event]
• HT : Getting H on first and T on second (= E₂)
• TH : Getting T on first and H on second (= E₃)
• TT : Getting T on first and T on second (= E₄)

Experimental (or empirical) probability

The experimental or empirical probability P(E) of an event is defined as

$P(E)=\frac{\text{Number of trials in which the event happened}}{\text{Total numbers of trials}}$ I.e., $P(E)=\frac{m}{n}$

Theoretical (or classical) probability

The theoretical or classical probability of an event E, written as P(E), is defined as

$P(E)=\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$

where the outcomes of the experiment are equally likely.

Impossible event (or null event)

An event is said to be an impossible event when none of the outcomes is favourable to the event. The probability of an impossible event = 0.

Important result

The probability of an event always lies between 0 and 1 i.e., $0\le P(E)\le 1.P(E)+P(\bar{E})=1$

Designation of playing cards

(i) A deck (pack) of cards contains 52 cards, out of which there are 26 red cards and 26 black cards.

(ii) There are four suits each containing 13 cards.

(iii) The cards in each suit are ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3 and 2.

(iv) Kings, queens and jacks are called face cards (4 + 4 + 4 = 12).

(v) Kings, queens, jacks and aces are called honour cards (4 + 4 + 4 + 4 = 1

4.0Solved Examples

Example 1: A coin is tossed twice. Find the probability of getting at least one head.

Solution: Sample space: {HH, HT, TH, TT} 

Favorable outcomes: {HH, HT, TH}

Probability =  ¾

Example 2: A letter of the English alphabet is chosen at random. Determine the probability that the letter is a consonant.

Solution: Total letters in the English alphabet (Sample space) = 26

No. of Consonants (Favourable outcomes) = 21

Probability = 21/26

Example 3: Box A contains 25 slips, of which 19 are marked Re 1 and others are marked Rs 5 each. Box B contains 50 slips, of which 45 are marked Re 1 each, and others are marked Rs 13 each. Slips of both boxes are poured into a third box and reshuffled. A slip is drawn at random. What is the probability that it is marked other than Re 1?

Solution: Total no. of slips in the third box (sample Space) = 75

No. slips marked as 1 re in the third box  = 64

No. of slips marked other than 1re in the third box = 75 - 64 = 11

Probability = 11/75

Example 4: A carton of 24 bulbs contains 6 defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced, and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

Solution: Total No. of Bulbs (sample space) = 24

No. of defective bulbs = 6

No. of bulbs that are not defective (Favourable outcome) = 18

Probability = 18/24 = 3/4

For second case: 

Total no. of Bulbs remaining (Sample Space)  = 25

No. of defective bulbs (Favourable outcome) = 5

Probability = 5/25 = 1/5

5.0Key Features of CBSE Class 10 Maths Notes Chapter 14 Probability

• Detailed Explanations: The notes provide a detailed breakdown of key concepts, such as sample spaces, events, and types of probability. Simple examples are used to clarify each concept.
• Formula Tables: All important formulas are summarised in an easily readable table format, which makes it ideal for quick revision before exams.
• Practice Problems: Students may test their understanding and hone their problem-solving abilities with the aid of the notes' practice problems, which range from simple to complex.
• Graphical Representation: Probability trees and Venn diagrams are used to visually represent difficult issues and promote comprehension.
• Exam-Aligned Content: To guarantee that students are fully prepared for exams, notes are created carefully in accordance with the CBSE syllabus, focussing primarily on high-weight themes.
• Real-World Applications: Real-life examples, such as calculating probabilities in games, lotteries, and weather predictions, make the topic relatable and engaging.
• Revision-Friendly Format: Important points, definitions, and formulae are highlighted for rapid revision. This facility proves to be very useful at the time of last minute preparation for exams.

Students may get a strong grasp of probability and feel comfortable tackling problems pertaining to this topic with the help of these CBSE mathematics notes for class 10, Chapter 14. Learning is comprehensive and in line with the standards of the CBSE test, thanks to thorough explanations, practice problems, and real-world applications.