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• Math Article
• Probability For Class 10

Probability Class 10 Notes Chapter 15

According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 14.

CBSE Class 10 Maths Probability Notes:- Download PDF Here

Class 10 maths chapter 15 probability notes.

CBSE Class 10 Maths Chapter 15 Probability Notes are provided here in detail. In this article, we are going to learn the definition of probability, experimental probability, theoretical probability and the different terminologies used in probability with complete explanations.

Students can refer to the short notes and MCQ questions along with separate solution pdf of this chapter for quick revision from the links below:

• Probability Short Notes
• Probability MCQ Practice Questions
• Probability MCQ Practice Solutions

What Is Probability?

The branch of mathematics that measures the uncertainty of the occurrence of an event using numbers is called probability. The chance that an event will or will not occur is expressed on a scale ranging from 0-1. It can also be represented as a percentage, where 0% denotes an impossible event and 100 % implies a certain event. Probability of an Event E is represented by P(E). For example, the probability of getting a head when a coin is tossed is equal to 1/2. Similarly, the probability of getting a tail when a coin is tossed is also equal to 1/2. Hence, the total probability will be: P(E) = 1/2 + 1/2 = 1 Know more about probability by clicking here .

Event and outcome

An Outcome is a result of a random experiment. For example, when we roll a dice getting six is an outcome. An Event  is a set of outcomes. For example, when we roll dice, the probability of getting a number less than five is an event. Note: An event can have a single outcome.

To know more about Types of Events, visit here .

Experimental Probability

Experimental probability can be applied to any event associated with an experiment that is repeated a large number of times. A trial is when the experiment is performed once. It is also known as empirical probability . Experimental or empirical probability: P(E) =Number of trials  where the event occurred/Total Number of Trials Example: In a day, a shopkeeper is able to sell 15 balls, out of which 6 were red balls. Find the probability of selling red balls on the next day of his sales. Given, the total number of balls sold = 15 Number of red balls sold = 6 Probability of red balls = 6/15 = 2/5

To know more about Experimental Probability, visit here .

Theoretical Probability

Theoretical Probability, P(E) = Number of Outcomes Favourable to E / Number of all possible outcomes of the experiment

Here we assume that the outcomes of the experiment are equally likely . Example: Find the probability of picking up a red ball from a basket that contains 5 red and 7 blue balls. Solution: Number of possible outcomes = Total number of balls = 5+7 = 12 Number of favourable outcomes = Number of red balls = 5 Hence, Probability, P(red) = 5/12

For more information on Probability, watch the below video

To know more about Theoretical Probability, visit here .

Elementary Event

An event having only one outcome of the experiment is called an elementary event . Example: Take the experiment of tossing a coin n number of times. One trial of this experiment has two possible outcomes: Heads(H) or Tails(T). So for an individual toss, it has only one outcome, i.e. Heads or Tails.

Sum of Probabilities

The sum of the probabilities of all the elementary events of an experiment is one . Example: take the coin-tossing experiment. P(Heads) + P(Tails )

=  (1/2)+ (1/2) =1

Impossible Event

An event that has a 100% probability of occurrence is called a sure event . The probability of occurrence of a sure event is one . E.g., What is the probability that a number obtained after throwing a die is less than 7? So,  P(E) = P(Getting a number less than 7) = 6/6= 1

Range of Probability of an event

Probability can range between 0 and 1, where 0 probability means the event to be an impossible one and probability of 1 indicates a certain event i.e. 0 ≤P (E) ≤ 1.

Geometric Probability

Complementary Events

Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails.

The best example of complementary events is flipping a coin, where ‘getting a head’ complement the event of ‘getting a tail’. To know more about Complementary Events, visit here .

Probability for Class 10 Examples

A bag contains only lemon-flavoured candies. Arjun takes out one candy without looking into the bag. What is the probability that he takes out an orange-flavoured candy?

Let us take the number of candies in the bag to be 100.

Hence, the probability that he takes out an orange-flavoured candy is:

P (Taking orange-flavoured candy) = Number of orange-flavoured candies / Total number of candies.

= 0/100 = 0

Hence, the probability that Arjun takes out an orange-flavoured candy is 0.

This proves that the probability of an impossible event is 0.

A game of chance consists of spinning an arrow that comes to rest, pointing at any one of the numbers such as 1, 2, 3, 4, 5, 6, 7, or 8, and these are equally likely outcomes. What is the probability that it will point at? (i)8 (ii) Number greater than 2 (iii) Odd numbers

Sample Space = {1, 2, 3, 4, 5, 6, 7, 8}

Total Numbers = 8

(i) Probability that the arrow will point at 8:

Number of times we can get 8 = 1

P (Getting 8) = 1/8.

(ii) Probability that the arrow will point at a number greater than 2:

Number greater than 2 = 3, 4, 5, 6, 7, 8.

No. of numbers greater than 2 = 6

P (Getting numbers greater than 2) = 6/8 = 3/4.

(iii) Probability that the arrow will point at the odd numbers:

Odd number of outcomes = 1, 3, 5, 7

Number of odd numbers = 4.

P (Getting odd numbers) = 4/8 = ½.

Related Articles:

• NCERT Solutions for Class 10 Maths Chapter 15 Probability
• Class 10 Maths Chapter 15 Probability MCQs
• Important Questions Class 10 Maths Chapter 15 Probability

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PROBABILITY.

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Probability

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Probability. 50-50 chance. likely. unlikely. poor chance. Independent Events. certain. possible. probable. Vocabulary. A sample space is the set of all possible outcomes . A simple example is flipping a coin. The sample space is {heads, tails}. Vocabulary.

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Probability 50-50 chance likely unlikely poor chance Independent Events certain possible probable

Vocabulary A sample space is the set of all possible outcomes. A simple example is flipping a coin. The sample space is {heads, tails}

Vocabulary Two events are independentif the outcome of one has no effect on the outcome of the other. Examples are rolling two dice, or spinning a spinner and rolling a dice

Vocabulary Two events are dependentif the outcome of one event relies on the other event. Examples are picking two marbles out of a bag, or two socks out of a drawer

3 4 Vocabulary The complement of an event is all the outcomes NOT included in the event. It is shown by A’. The following spinner is spun once: What is the probability of it not landing on the yellow sector? P(not yellow) OR P(yellow’) =

Vocabulary The intersection of two events is all the outcomes that are SHARED by both events. It is denoted by A∩B and can be read A and B Event A is even numbers on a dice Event B is multiples of 3 on a dice A ∩B is the number 6 P(A ∩B) = 1/6 If two events are independent, then their intersection can be calculated as P(A ∩B)=P(A)*P(B)

Vocabulary The union of two events is all the outcomes of either event events. It is denoted by AUB and can be read A or B. Event A is odd numbers on a dice Event B is multiples of 3 on a dice A UB is {1,3,5,6} P(AUB) = 4/6 or 2/3 Union can be calculated as P(AUB)=P(A)+P(B)- P(A∩B)

Consider a marriage or union of two people – when two people marry, what do they do with their possessions ? This symbol means “union” The bride takes all her stuff & the groom takes all his stuff & they put it together! And live happily ever after! This is similar to the union of A and B. All of A and all of B are put together!

The two spinners are spun. What is the probability that both spinners will show an even number? P(1st spinner even) = 4 8 P(2nd spinner even) = 4 8 P(both spinners even) =4 ∙ 4 = 1 8 8 4 Example

A game uses a dice and a spinner. A player rolls a dice. What is the P(odd #)? The player spins the spinner. What is the P(red)? 3. What is the P(odd # and Red)? Example

There are 4 red, 8 yellow and 6 blue socks in a drawer. Once a sock is selected it is not replaced. Find the probability that 2 blue socks are chosen. P(1st blue sock) = 6 18 P(2nd blue sock) = 5 17 P(Two blue socks) = 6 ∙ 5 = 5 18 17 51 Example # of socks after 1 blue is removed Total # of socks after 1 blue is removed

Example • In a certain town, the probability that a person plays sports is 65%. The probability that a person is between the ages of 12 and 18 is 40%. The probability that a person plays sports and is between the ages of 12 and 18 is 25%. Are the events independent?

Outcomes are mutually exclusive if they cannot happen at the same time. Mutually exclusive outcomes For example, when you toss a single coin either it will land on heads or it will land on tails. There are two mutually exclusive outcomes. Outcome A: Head Outcome B: Tail

Outcome A: the pupil has brown eyes. Outcome B: the pupil has blue eyes. Outcome C: the pupil has black hair. Outcome D: the pupil has wears glasses. A pupil is chosen at random from the class. Which of the following pairs of outcomes are mutually exclusive? Mutually exclusive outcomes These outcomes are mutually exclusive because a pupil can either have brown eyes, blue eyes or another colour of eyes. These outcomes are not mutually exclusive because a pupil could have both black hair and wear glasses.

For example, a game is played with the following cards: 2 1 1 1 1 and P(sun) = 3 3 3 3 3 + = If two outcomes are mutually exclusive then their probabilities can be added together to find their combined probability. Adding mutually exclusive outcomes What is the probability that a card is a moon or a sun? P(moon) = Drawing a moon and drawing a sun are mutually exclusive outcomes so, P(moon or sun) = P(moon) + P(sun) =

For example, a game is played with the following cards: 1 1 and P(star) = 3 3 If two outcomes are mutually exclusive then their probabilities can be added together to find their combined probability. Adding mutually exclusive outcomes What is the probability that a card is yellow or a star? P(yellow card) = Drawing a yellow card and drawing a star are not mutually exclusive outcomes because a card could be yellow and a star. P (Y U S) = P(Y) + P(S) – P(Y∩S) = 1/3 + 1/3 – 1/9 = 5/9.

Venn Diagrams • Venn diagrams are useful in figuring out probabilities P(AUB)’

Example • If A is the students who own bikes and B is the students who own skateboards, find • A∩B and P(A∩B). Are the events independent? • AUB and P(AUB) • (AUB)’ and P(AUB)’

20 The “eggs” show Math and Biology Ex. Amongst a group of 20 students, 7 are taking Math and of these 3 are also taking Biology. 5 are taking neither. What is the probability that a student chosen at random is taking Biology? Solution: The diagram shows the 20 students. B M 4 3 3 do both 5 do neither 5 7 take Math ( but we have 3 already )

20 Amongst a group of 20 students, 7 are taking Maths and of these 3 are also taking Biology. 5 are taking neither. What is the probability that a student chosen at random is taking Biology? Solution: The diagram shows the 20 students. B M The final number (taking Biology but not Math ) is given by 4 3 8 5 So, P( student takes Biology ) =

Filling in a Venn diagram 100 people are asked if they eat meat, fish, both, or neither. You are told that 55 eat meat, 52 eat fish, and 21 eat neither. Use this information to complete the Venn diagram below. 21 eat neither 27 28 24 21

Finding probabilities Use the Venn diagram to find the probability that someone picked at random: a) eats meat, b) eats fish, c) eats neither, d) eats only fish, e) eats both. ‘Given that’ Given that a man eats meat, find the probability that he also eats fish.

The “and” rule Summary of methods The “or” rule • The word “or” often indicates that the probabilities need to be added together. • P(A or B) = P(AUB) = P(A) + P(B) – P(A∩B) • The word “and” often indicates that the probabilities need to be multiplied together. • P(A and B) = P(A∩B) = P(A) × P(B) if the two events are independent.

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One of the primary advantages of using PowerPoint presentations in mathematics class is their ability to serve as a visual aid. Complex mathematical concepts and formulas can be challenging to grasp through traditional methods alone. However, with the use of visuals, diagrams, and animations, PPTs can make abstract mathematical ideas more concrete and understandable for students. Visuals help students visualize mathematical problems, making it easier for them to grasp the underlying concepts.

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Introducing Probability

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