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Probability Class 10th Notes - Free NCERT Class 10 Maths Chapter 15 Notes - Download PDF

Probability Class 10th Notes - Free NCERT Class 10 Maths Chapter 15 Notes - Download PDF

Updated on Apr 19, 2025 12:36 PM IST

Probability is the branch of mathematics that deals with randomness and uncertainty. In general terms, probability is defined as possibilities. It is expressed as a number between 0 and 1. It has been introduced to determine how different outcomes arrive in uncertain situations. It is used in various fields such as science, finance, artificial intelligence, statistics, decision making, etc. Generally, probability means the extent to which something is likely to happen. The concept of probability occurs from the games of chance, but now it's evolved into a rigorous mathematical discipline. It helps us to answer questions like, what is the chance of getting tails during flipping a coin? Or what is the probability of getting 6 while rolling a dice? Etc. Now, to answer these, we should know the total number of possible outcomes. The basic theory of probability is also used in the probability distribution, where we will learn to determine the possible outcomes for the random experiments.

This Story also Contains
  1. NCERT Notes Class 10 Maths Chapter 14 Probability
  2. What is Probability?
  3. Experimental Probability
  4. Theoretical Probability
  5. Key Points
  6. Key Terms in Probability:
  7. Class 10 Chapter Wise Notes
  8. NCERT Exemplar Solutions for Class 10
  9. NCERT Solutions for Class 10
  10. NCERT Books and Syllabus
Probability Class 10th Notes - Free NCERT Class 10 Maths Chapter 15 Notes - Download PDF
Probability Class 10th Notes - Free NCERT Class 10 Maths Chapter 15 Notes - Download PDF

CBSE Class 14 chapter Probability also includes a definition of probability? 'How do we calculate the probability of a single event or multiple events?', 'What are the different types of probability? These topics can be easily downloaded from the Class 10 Maths chapter 14 notes PDF. Along with this, NCERT class 10th maths notes serve as your principal resource for exam preparation, and the NCERT Notes facilitate linking present educational content to both prior lessons and upcoming material.

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NCERT Notes Class 10 Maths Chapter 14 Probability

What is Probability?

Probability is defined as a measure of the possibility or chance that a particular event will occur. It assesses uncertainty and is used to determine the outcomes in various situations, from everyday life to scientific research.

Probability is expressed as a number between 0 and 1, which implies 0 means an event is impossible (e.g., rolling an 8 on a standard dice) and 1 means an event is certain (e.g., the sun rising tomorrow). In other terms, it is also represented as a percentage, where 100% means a specific event and 0% means an impossible event. A probability between 0 and 1 represents the degree of possibility of an event occurring. Probability of an Event E is represented by P(E).

Experimental Probability

Experimental Probability is founded on real-world observations and experimentation. It applies to any occurrence related to an experiment that is carried out numerous times.

The Experimental probability is calculated as follows:

P(E) = Number of trials in which the event happenedTotal number of trials

Theoretical Probability

Theoretical Probability is calculated by mathematical methods instead of experimental research or without conducting experiments.

For an event E, the theoretical probability is calculated as follows:

P(E) = Number of favorable outcomesTotal number of possible outcomes

Examples of Probability

  1. Tossing of a Coin: When a coin is tossed, the probability of getting heads is:

    P(E) = Number of favorable outcomesTotal number of possible outcomes

    Here, favourable outcomes are 1 (because in a coin, heads is one in count)

    And, the total number of possible outcomes is 2 (one is heads and the other is tails)

    So, P(Heads) = 12 = 0.5

  2. Rolling a Dice: When a dice is rolled, the probability of getting 4 is:

    In this case, favourable outcomes are 1 (because on a dice, 4 comes only once)

    And, the total number of possible outcomes is 6 (there are 6 numbers on a dice)

    So, P(4) = 16=0.1666$

  3. Drawing a Black Card from a Deck: There are 52 cards in a deck, 26 of which are black. The probability of drawing a black card is:

    P(Black Card) = 2652=12=0.5
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People use probability for multiple purposes, including statistics and gaming as well as finance and artificial intelligence for deciding and predicting future risks.

Key Points

  • The expression of probability exists between 0 and 1. It means:

0 ≤ P(E) ≤ 1 for any Event E

  • Any event with a probability value of 0 is completely impossible.
  • When an event carries a probability value of 1, it indicates a certain occurrence.
  • When an event stands between 0 and 1, it demonstrates how probable the event is to happen.
  • An event having only one outcome of the experiment is called an elementary event. Like, in the case of tossing a coin, there is only one outcome, either heads or tails.
  • The sum of the probabilities of all the elementary events of an experiment is 1. Take an example of tossing a coin:

P(heads) = 0.5
P(tails) = 0.5

They are both elementary events.
So, P(heads) + P(tails) = 0.5 + 0.5 = 1

Key Terms in Probability:

Experiment:

A process generates various possible end results (e.g., rolling a die).

Sample Space (S):

The set of all possible outcomes of an experiment (e.g., {1, 2, 3, 4, 5, 6} for a die roll) is called as Sample Space.

For example,
A coin is tossed, and it is called an Event.
E1 = Having a head (H) on the upper face when tossed.
E2 = Having a tail (T) on the upper face when tossed.
So, in this case, the possible outcomes are Heads or Tails
Therefore, S = {H, T}

Event (E):

A subset of possible experimental outcomes which shows particular outcomes or collections of outcomes (e.g., rolling an even number).

Probability of an Event [P(E)]:

A measure of the likelihood of an event occurring, calculated as:

P(E)=Number of favorable outcomesTotal number of possible outcomes

Complementary Events:

The probability of an event not occurring is called the complementary event.

P(E)=1P(E)

The event E, representing ‘not E’, is called the complement of the event E. It means E and E are complementary events.

For example, Flipping of a Coin, where ‘getting a tail’ complemented the event of ‘getting a head’.

Elementary Events:

An event having only one outcome of the experiment is called an Elementary Event.

For example, when rolling a six-sided die, the sample space is:

S = {1, 2, 3, 4, 5, 6}

In this case, each outcome (1, 2, 3, 4, 5, or 6) is an elementary event because it consists of a single outcome.

Like,
Getting a 1 → E = {1}
Getting a 4 → E = {4}

Each of these events has a probability of: P(E) = 16

Impossible Event:

An impossible event describes any outcome which will never occur within a particular experiment. It holds true that every impossible event will have a probability value of zero.

For example, the probability of getting a number 8 in a single throw of a die is 0. As 8 can never be the outcome.

Sure Event:

A sure event stands as an event which necessarily occurs throughout a particular experiment. A sure event (certain event) holds a fixed probability value of one.

For example, the probability of getting a number less than 7 in a single throw of a die is 1 because it is certain that when a die is thrown once, we will always receive a number less than seven. After all, each face of the die is marked with a number less than seven. Thus, there are six alternative outcomes, which is the same number of favorable options.

The comprehension of probability remains essential for satisfying decision-making processes when uncertainty exists in domains of finance, games, science and technology. Statistical inference, along with machine learning, stands upon probability as its basis, therefore making probability an essential mathematical concept linked to various domains.

Class 10 Chapter Wise Notes

Students must download the notes below for each chapter to ace the topics.


NCERT Exemplar Solutions for Class 10

Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.

NCERT Solutions for Class 10

Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.

NCERT Books and Syllabus

To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.

Frequently Asked Questions (FAQs)

1. What is Probability in Class 10 Maths?

Probability is defined as a measure of the possibility or chance that a particular event will occur. It assesses uncertainty and is used to determine the outcomes in various situations, from everyday life to scientific research. Probability is expressed as a number between 0 and 1.

2. What are the Basic Formulas of Probability in Class 10?

The fundamental formula for probability is: P(E) = Number of favorable outcomesTotal number of possible outcomes

Other important formulas include:

Probability of an event not occurring: P(E)=1P(E)

Sum of all probabilities of an experiment: P(E1) + P(E2) + ... + P(En) = 1

3. Can Probability Be Greater Than 1?

No, probability always lies between 0 and 1 and can also be equal to 0 or 1.

4. What is a Sample Space in Probability?

The set of all possible outcomes of an experiment (e.g., {1, 2, 3, 4, 5, 6} for a die roll) is called as Sample Space.

5. How Do You Calculate the Probability of Getting at Least One Head in Two Coin Tosses?

In this case, sample space: {HH, HT, TH, TT}

Favorable cases (at least one H): {HH, HT, TH}

Probability = Number of favorable outcomesTotal number of possible outcomes

= 34

6. How Do You Calculate the Probability of Getting at Least One Head in Two Coin Tosses?

In this case, sample space: {HH, HT, TH, TT}

Favorable cases (at least one H): {HH, HT, TH}

Probability = Number of favorable outcomesTotal number of possible outcomes

= 34

Articles

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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