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NCERT Solutions for Exercise 13.1 Class 12 Maths Chapter 13 Probability are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 13.1 Class 12 Maths chapter 13 is very important for the students who wish to perform well in the 12th board exam. NCERT book exercise has covered topics like the probability of events, conditional probability, properties of conditional property, etc. Probability has a lot of real-life applications like forecasting the weather, sports, online gaming, insurance, politics lottery tickets, playing cards, statistics, etc. There area total of 17 questions covered in the exercise 13.1 Class 12 Maths which are mostly related to conditional probability. You are advised to solve all these NCERT syllabus problems on your own. You can go through NCERT solutions for Class 12 Maths chapter 13 exercise 13.1 If you are facing difficulties while solving these problems.
12th class Maths exercise 13.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise enumerated in NCERT Book together using the link provided below.
Also, see
Answer:
It is given that and
Question:6 A coin is tossed three times, where
(i)E : head on third toss ,F : heads on first two tosses
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: head on third toss, F: heads on first two tosses
Question:6 A coin is tossed three times, where
(ii)E : at least two heads ,F : at most two heads
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E : at least two heads , F : at most two heads
Question:6 A coin is tossed three times, where
(iii)E : at most two tails ,F : at least one tail
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: at most two tails, F: at least one tail
Question:7 Two coins are tossed once, where
(i) E : tail appears on one coin, F : one coin shows head
Answer:
E : tail appears on one coin, F : one coin shows head
Total outcomes =4
Question:7 Two coins are tossed once, where
(ii)E : no tail appears,F : no head appears
Answer:
E : no tail appears, F : no head appears
Total outcomes =4
Question:8 A die is thrown three times,
E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Answer:
E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Total outcomes
Question:9 Mother, father and son line up at random for a family picture
E : son on one end, F : father in middle
Answer:
E : son on one end, F : father in middle
Total outcomes
Let S be son, M be mother and F be father.
Then we have,
Question:10 A black and a red dice are rolled.
(a) Find the conditional probability of obtaining a sum greater than , given that the black die resulted in a
Answer:
A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum greater than and B be a event that the black die resulted in a
Question:10 A black and a red dice are rolled.
(b) Find the conditional probability of obtaining the sum , given that the red die resulted in a number less than .
Answer:
A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum 8 and B be a event thatthat the red die resulted in a number less than .
Red dice is rolled after black dice.
Question:11 A fair die is rolled. Consider events and Find
(i) and
Answer:
A fair die is rolled.
Total oucomes
and
Question:11 A fair die is rolled. Consider events and Find
(ii) and
Answer:
A fair die is rolled.
Total oucomes
,
Question:11 A fair die is rolled. Consider events and Find
(iii) and
Answer:
A fair die is rolled.
Total oucomes
and
,
(i) the youngest is a girl,
Answer:
Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and B= the youngest is a girl =
Therefore, the required probability is 1/2
(ii) at least one is a girl?
Answer:
Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and C= at least one is a girl =
Answer:
An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions.
Total number of questions
Let A = question be easy.
Let B = multiple choice question
easy multiple questions
Therefore, the required probability is 5/9
Answer:
Two dice are thrown.
Total outcomes
Let A be the event ‘the sum of numbers on the dice is 4.
Let B be the event that two numbers appearing on throwing two dice are different.
Therefore, the required probability is 1/15
Answer:
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin.
Total outcomes
Total number of outcomes =20
Let A be a event when coin shows a tail.
Let B be a event that ‘at least one die shows a 3’.
Question:16 In the following Exercise 16 choose the correct answer:
If then is
(A)
(B)
(C)
(D)
Answer:
It is given that
Hence, is not defined .
Thus, correct option is C.
Question:17 In the following Exercise 17 choose the correct answer:
If and are events such that then
(A) but
(B)
(C)
(D)
Answer:
It is given that
Hence, option D is correct.
Exercise 13.1 Class 12 Maths solutions are consist of questions related to conditional probability and different properties of conditional probability. There are 15 short answer type questions and 2 multiple choice types questions are given in this exercise. There are 7 solved examples given in the NCERT textbook before this exercise that is related to conditional probability. You can solve these examples before solving exercise problems, so it will be easy for you to solve exercise problems.
Also Read| Probability Class 12th Notes
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Happy learning!!!
Probability has 10 marks weightage in the CBSE Class 12 Maths final board exam.
There are 6 exercises including a miscellaneous exercise in the NCERT Class 12 Maths chapter 13 Probability.
There are 17 questions in NCERT Class 12 Maths chapter 13 exercise 13.1.
Here you will get NCERT Exemplar Solutions for Class 12 Maths Probability.
The conditional probability of an event is the probability of that event given that the other event happened
Two events are called independent events if they exist such that the probability of occurrence of one event is not dependent on the occurrence of another event.
If the probability of occurrence of an event is zero then such event is called a null event.
An event is said to be a certain event when all possible outcomes are favorable to the event.
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Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
Possible steps:
Re-evaluate Your Study Strategies:
Consider Professional Help:
Explore Alternative Options:
Focus on NEET 2025 Preparation:
Seek Support:
Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.
I hope this information helps you.
Hi,
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
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