## Ncert Solutions For Class 12 Maths Chapter 13

Refer to Probability Class 12 NCERT Solutions available on Vedantu for detailed understanding on probability, which is an important topic in Class 12 Mathematics. Students will learn the basic principles of probability and get a strong base of Chapter 13 Class 12 Maths when they refer to our solutions. Our well-designed NCERT Solutions for Class 12 Maths Chapter 13 have been prepared by knowledgeable teachers and the subject matter experts who have tried to explain this vast concept in as simple terms as possible.

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## Key Features Of Ncert Solutions For Class 12 Maths Chapter 13

Studying the chapter Probability of Class 12 NCERT Solutions enables the students to understand Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes theorem, Random variable and its probability distribution, mean and variance of a random variable.

## Big Ideas Math Geometry Answers Chapter 12 Probability

Big Ideas Math Book Geometry Answer Key Ch 12 Probability is aligned as per the BIM Geometry Textbooks. Refer to the BIM Geometry Solutions for quick guidance on the Topicwise Concepts of Probability. Big Ideas Math Geometry Solution Key can be downloaded for free of cost. Access the Big Ideas Math Geometry Chapter 12 Probability Answers created by subject experts adhering to the latest Common Core State Standards guidelines. Download the handy resources for Big Ideas Math Geometry Chapter 12 Probability Solutions and begin your preparation.

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## Cbse Test Papers Class 12 Mathematics Probability

CBSE chapter wise practice papers with solution for class 12 Mathematics chapter 13 Probability for free download in PDF format. 12th Mathematics chapter 13 Probability have many topics. All these topics are included in CBSE solved test papers of class 12 Mathematics chapter Probability. CBSE solved test papers and chapter wise question papers for practice with solution have plenty of questions for daily practice and smart study.

## Ition Of A Sample Space H3

This Probability NCERT Solutions Class 12 section explains what partition of sample space is. Set of events say E1, E2, , En represents the partition of sample space S is if

The events E1, E2, , En represent a partition of the sample space S if they are pairwise disjoint, are exhaustive and have nonzero probabilities.

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## Ncert Solutions For Class 12 Maths Chapter 13 Probability

Given that E and F are events such that P = 0.6, P = 0.3 and P = 0.2, find P and P.

If P = 6/11, P = 5/11 and and P = 7/11 find

A coin is tossed three times, where E: head on third toss, F: heads on first two tosses

A coin is tossed three times, where E: at least two heads, F: at most two heads

A coin is tossed three times, where E: at most two tails, F: at least one tail

Two coins are tossed once, where E: tail appears on one coin, F: one coin shows head

A die is thrown three times, E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses

Mother, father and son line up at random for a family picture E: son on one end, F: father in middle

A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

A fair die is rolled. Consider events E = , F = and G = Find P and P

A fair die is rolled. Consider events E = , F = and G = Find P and P

A fair die is rolled. Consider events E = , F = and G = Find P |G) and P |G)

Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event the sum of numbers on the dice is 4.

A = B

## Cbse Question Papers 12th Mathematics Chapter 13

CBSE papers with answers and Probability for chapter 13 Probability class 12th Mathematics includes practice question papers with 10-12 questions in each test paper. There are around 3-5 solved test papers in each chapter. Thus, users will get around 30-50 very important questions from each chapter in form of CBSE test papers with complete solution and answers. The question papers and CBSE with Probability practice papers for 12 Mathematics, Probability are very helpful for students who wish to get good marks in exams.

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## Exercise 124 Probability Of Disjoint And Overlapping Events

Vocabulary and Core Concept Check

Question 1.**WRITING**Are the events A and \ disjoint? Explain. Then give an example of a real-life event and its complement.Answer:Yes A and \ are disjoint events because they are the complement of one another and so can not occur together and hence the name disjoint.Example:So, A = \ = are disjoint events.

Question 2.Which is different? Find both answers.How many outcomes are in the intersection of A and B?Answer: There are 2 outcomes in the intersection of A and B.

How many outcomes are shared by both A and B?Answer: 2 outcomes are shared by both A and B.

How many outcomes are in the union of A and B?Answer: There are 4 + 2 + 3 = 9 outcomes in the union of A and B.

How many outcomes in B are also in A?Answer: There are 2 outcomes in B that are also in A.

Monitoring progress and Modeling with Mathematics

In Exercises 3 6, events A and B are disjoint. Find P

Question 3.

P = P + PP = 0.55 + 0.2 = 0.75

Question 5.P = \, P = \Answer:

p = \, P = \Answer:p = \, P = \P = P + PP = \ + \P = \

Question 7.**PROBLEM SOLVING**Your dart is equally likely to hit any point inside the board Shown. You throw a dart and pop a balloon. What is the probability that the balloon is red or blue?Answer:

**ERROR ANALYSIS**In Exercises 11 and 12, describe and correct the error in finding the probability of randomly drawing the given card from a standard deck of 52 playing cards.

Question 11.

In Exercises 13 and 14, you roll a six-sided die. Find P.

Writing a Conjecture

## Big Ideas Math Book Geometry Answer Key Chapter 12 Probability

Make the most out of the Big Ideas Math Geometry Answer Key for Cha 12 Probability and score better grades in the exams. Simply tap on the quick links available and prepare the respective topics available as and when you need them. Big Ideas Math Geometry Answers Chapter 12 Probability available here covers questions from the Topics Sample Spaces, Independent and Dependent Events, Disjoint and Overlapping Events, Binomial Distributions, Probability Test, etc.

Taking the inverse of both sidesx%/100% = 34.4/86Therefore, 34.4 is 40% of 86.

Display the data in a histogram.

Question 4.

Question 5.**ABSTRACT REASONING**You want to purchase either a sofa or an arm chair at a furniture store. Each item has the same retail price. The sofa is 20% off. The arm chair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair. Are the items equally priced after the discounts arc applied? Explain.Answer: Yes

Explanation:You want to purchase either a sofa or an armchair at a furniture store.Each item has the same retail price. The sofa is 20% off. The armchair is 10% off. and you have a coupon to get an additional 10% off the discounted price of the chair.The price of armchair and sofa are the same.If you add 10% to chair the discount for the chair and sofa will be the same.10% + 10% = 20%

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## Probability Distribution Of A Random Variable

The probability distribution of a random value is what defines the probability of its value that is unknown. The random variable could either be discrete or continuous. They can also be both.

There can be two random variables with an equal probability distribution and yet they can vary with how they are in respect to the other random variables or whether they are independent of the random variables. The recognition of the outcome of the value that is randomly chosen as per the probability distribution of the variable is the random variate.

For any event of any random experiment, it is possible to find its corresponding probability. Even for the different random variable values, it is possible to find its respective probability. The probability distribution of the random variable is the value of the random variable along with its corresponding probabilities.

Properties of Probability Distribution

The probability distribution of a random variable is explained in Class 12 Maths Ch 13 NCERT solutions where X is P = pi for x = xi and P = 0 for x xi.

The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 p 1.

## Chapter 13 Solutions In Pdf

#### Previous Years Questions

##### Important Questions for practice

###### Questions from Board Papers

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## Exercise 121 Sample Spaces And Probability

Vocabulary and Core Concept Check

Question 1.A number that describes the likelihood of an event is the ___________ of the event.Answer:A number that describes the likelihood of an event is the Probability of the event.

Question 2.**WRITING**Describe the difference between theoretical probability and experimental probability.Answer: Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.

Monitoring Progress and Modeling with Mathematics

In Exercises 3 6. find the number of possible outcomes in the sample space. Then list the possible outcomes.

Question 3.You roll a die and flip three coins.Answer:

Question 4.You flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.Answer:Given data,You flip a coin and draw a marble at random from a hag containing two purple marbles and one while marble.the probability of getting a purple marble = 2/3the probability of getting a white marble = 1/3

Question 5.A bag contains four red cards numbered 1 through 4, four white cards numbered 1 through 4, and four black cards numbered 1 through 4. You choose a card at random.Answer:

Question 7.**PROBLEM SOLVING**A game show airs on television five days per week. Each day, a prize is randomly placed behind one of two doors. The contestant wins the prize by selecting the correct door. What is the probability that exactly two of the five contestants win a prize during a week?Answer:

Question 29.\Answer:

## Lesson 121 Sample Spaces And Probability

**Monitoring Progress**

Find the number of possible outcomes in the sample space. Then list the possible outcomes.

Question 1.Answer: 4

Explanation:When we flip two coins simultaneoulsy then the possible outcomes will be , , , where H represents headsThus the possible outcomes are 2² = 4

Question 2.You flip two Coins and roll a six-sided die.Answer: 6 × 2² = 24

Explanation:We roll a die and flip two coins. We have to find the number of possible outcomes in this space. Also we have to list the possible outcomes.1 = 2 = 3 = 4 = 5 = 6 = On the other hand, using H for Heads and T for Tails we can list the outcomes., , , , , , , , , , , , , , , , , , , , Therefore, we can conclude that the number of all possible outcomes is6 × 2² = 24

Question 3.You flip a coin and roll a six-sided die. What is the probability that the coin shows tails and the die shows 4?Answer:The sample space has 12 possible outcomes.Heads, 1

More likely to get 2 points.

Question 10.In Example 5, for which color is the experimental probability of stopping on the color greater than the theoretical probability?Answer:9/20 = 0.45

Question 11.In Example 6, what is the probability that a pet-owning adult chosen at random owns a fish?Answer:

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## Mean Of A Random Variable

If X is a random variable and has the possible valued like x1,x2,x3,,xn occurring with probabilities p1,p2,p3,,pn, respectively, the mean of the random variable denoted by is the weighted average of the possible values of X. Each of the values is weighted by the probability with which it occurs.

The mean of a random variable can also be said as the expectation of X.

E = = i=1n xipi

=x1p1 + x2p2 + + xnpn

## Cbse Class 12 Maths Chapter

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 13 Probability prepared by expert Maths teachers from latest edition of CBSE books, On CoolGyan.Org to score more marks in CBSE board examination. You can also Download __Maths Revision Notes Class 12__ to help you to revise complete Syllabus and score more marks in your examinations.

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## Ncert Solutions For Class 12 Maths Free Pdf Download

You can now get the Probability Class 12 NCERT Book Solutions PDF Download for free on Vedantu, so you can refer to it whenever you wish to. The Probability Class 12 PDF solutions are handy, which means that whenever you have any doubts on any topic on probability, you can refer to the solutions to get your concepts cleared. Every solution is solved in detailed steps to explain the concept well to you.

## Lesson 122 Independent And Dependent Events

**Monitoring progress**

Question 1.In Example 1, determine whether guessing Question 1 incorrectly and guessing Question 2 correctly are independent events.Answer:

Question 2.In Example 2, determine whether randomly selecting a girl first and randomly selecting a boy second are independent events.Answer:

Question 3.In Example 3, what is the probability that you spin an even number and then an odd number?Answer:

In Example 4, what is the probability that both hills are $1 hills?Answer:

Question 5.In Example 5, what is the probability that none of the cards drawn are hearts when you replace each card, and you do not replace each card? Compare the probabilities.Answer: you replace each card,P = P P P= 13/52 . 13/52 . 13/52 = 1/4 . 1/4 . 1/4 = 1/64 = 0.016

Question 6.In Example 6, find the probability that a non-defective part passes and the probability that a defective part fails.Answer: the probability that a non-defective part passesP = 3/39 = 1/13 = 0.077 the probability that a defective part fails.P = 11/461 = 0.024

Question 7.At a coffee shop. 80% of customers order coffee. Only 15% of customers order coffee and a bagel. What is the probability that a customer who orders coffee also orders a bagel?Answer:B: Customer order a bagelP = P/P80% of customers order coffee and Only 15% of customers order coffee and a bagel.P = 80/100 = 0.8P = 15/100 = 0.15P = P/P = 0.15/0.8 = 0.1875 = 18.75%

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## Lesson 125 Permutations And Combinations

**Monitoring Progress**

In how many ways can you arrange the letters in the word HOUSE?Answer:

In how many ways can you arrange 3 of the letters in the word MARCH?Answer:

Question 3.**WHAT IF**In Example 2, suppose there are 8 horses in the race. In how many different ways can the horses finish first, second, and third? Answer:

Question 4.**WHAT IF?**In Example 3, suppose there are 14 floats in the parade. Find the probability that the soccer team is first and the chorus is second.Answer:

Question 5.Count the possible combinations of 3 letters chosen from the list A, B, C, D, E.Answer:

Question 6.**WHAT IF?**In Example 5, suppose you can choose 3 side dishes out of the list of 8 side dishes. How many combinations are possible?Answer:

Question 7.**WHAT IF?**In Example 6, suppose there are 20 photos in the collage. Find the probability that your photo and your friends photo are the 2 placed at the top of the page.Answer:

## Daily Class Assignments Quizzes And Test Dates

Text to #: 81010 with the following message:

__1st Period__ @**9669fc**

- Tuesday, August 8th – Section 1.1
- Wednesday, August 9th -Section 1.2
- Thursday, August 10th – Section 1.3
- Friday, August 11th – Section 1.3

- Monday, August 14th – Summer Work Test
- Tuesday, August 15th – Section 1.4
- Wednesday, August 16th – Section 1.4/1.5
- Thursday, August 17th – Section 1.5
- Friday, August 18th – Section 1.6

- Monday, August 21st – Review sections 1 – 5
- Tuesday, August 22nd – Section 1.7
- Wednesday, August 23rd – Constructions
- Thursday, August 24th – Chapter 1 Review Game
- Friday, August 25th – Chapter 1 Test

- Monday, August 28th – Section 2.1
- Tuesday, August 29th – Section 2.2
- Wednesday, August 30th – Section 2.3
- Thursday, August 31st – Section 2.4
- Friday, September 1st – Section 2.5

- Monday, September 4th – NO SCHOOL – LABOR DAY
- Tuesday, September 5th – Section 2.6
- Wednesday, September 6th – Section 2.7
- Thursday, September 7th – Finish 2.7
- Friday, September 8th – Section 2.8

- Monday, September 11th – Finish 2.8
- Tuesday, September 12th – Review Proofs
- Wednesday, September 13th – Chapter 2 Review
- Thursday, September 14th – Chapter 2 Test
- Friday, September 15th – NO SCHOOL FOR STUDENTS

- Monday, September 18th – Section 3.1
- Tuesday, September 19th – Section 3.2
- Wednesday, September 20th – Section 3.5
- Thursday, September 21st – Section 3.3
- Friday, September 22nd – Section 3.4

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