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NCERT Solutions for miscellaneous exercise chapter 13 class 12 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 Class 12 Maths chapter 13 miscellaneous exercise consist of different types of questions covering all the concepts of probability Class 12 Maths NCERT syllabus. These questions can be practised, if you have solved all the previous NCERT book chapter 13 exercises. Miscellaneous exercise chapter 13 Class 13 questions are a bit difficult than all the previous exercises questions. You are advised to solve all exercise questions by yourself. If you find difficulties while solving them, you can go through NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise.
There are very few questions asked in the board exams from miscellaneous exercises, it is not considered to be very important for board exams. You can solve these exercises to be on the safer side in the board exams. Miscellaneous exercise class 12 chapter 13 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.
Question:1(i) A and B are two events such that Find if
is a subset of
Answer:
A and B are two events such that
Question:2(i) A couple has two children,
Find the probability that both children are males, if it is known that at least one of the children is male.
Answer:
A couple has two children,
sample space
Let A be both children are males and B is at least one of the children is male.
Question:2(ii) A couple has two children,
Find the probability that both children are females, if it is known that the elder child is a female.
Answer:
A couple has two children,
sample space
Let A be both children are females and B be the elder child is a female.
Answer:
We have of men and of women have grey hair.
Percentage of people with grey hairs
The probability that the selected haired person is male :
Answer:
of people are right-handed.
at most of a random sample of people are right-handed.
the probability that more than of a random sample of people are right-handed is given by,
the probability that at most of a random sample of people are right-handed is given by
.
all will bear mark.
Answer:
Total balls in urn = 25
Balls bearing mark 'X' =10
Balls bearing mark 'Y' =15
balls are drawn with replacement.
Let Z be a random variable that represents a number of balls with Y mark on them in the trial.
Z has a binomial distribution with n=6.
not more than will bear mark.
Answer:
Total balls in urn = 25
Balls bearing mark 'X' =10
Balls bearing mark 'Y' =15
balls are drawn with replacement.
Let Z be random variable that represents number of balls with Y mark on them in trial.
Z has binomail distribution with n=6.
the number of balls with mark and mark will be equal.
Answer:
Answer:
Let p and q respectively be probability that the player will clear and knock down the hurdle.
Let X represent random variable that represent number of times the player will knock down the hurdle.
Answer:
Probability of 6 in a throw of die =P
Probability that 2 sixes come in first five throw of die :
Probability that third six comes in sixth throw :
Question:8 If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?
Answer:
In a leap year, there are 366 days.
In 52 weeks, there are 52 Tuesdays.
The probability that a leap year will have 53 Tuesday is equal to the probability that the remaining 2 days are Tuesday.
The remaining 2 days can be :
1. Monday and Tuesday
2. Tuesday and Wednesday
3. Wednesday and Thursday
4. Thursday and Friday
5.friday and Saturday
6.saturday and Sunday
7.sunday and Monday
Total cases = 7.
Favorable cases = 2
Probability of having 53 Tuesday in a leap year = P.
Answer:
Probability of success is twice the probability of failure.
Let probability of failure be X
then Probability of success = 2X
Sum of probabilities is 1.
Let and
Let X be random variable that represent the number of success in six trials.
Answer:
Let the man toss coin n times.
Probability of getting head in first toss = P
The minimum value to satisfy the equation is 4.
The man should toss a coin 4 or more times.
Answer:
In a throw of die,
probability of getting six = P
probability of not getting six = q
There are three cases :
1. Gets six in the first throw, required probability is
The amount he will receive is Re. 1
2.. Does not gets six in the first throw and gets six in the second throw, then the probability
The amount he will receive is - Re.1+ Re.1=0
3. Does not gets six in first 2 throws and gets six in the third throw, then the probability
Amount he will receive is -Re.1 - Re.1+ Re.1= -1
Expected value he can win :
Question:12(i) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A ?
Answer:
'
Let R be the event of drawing red marble.
Let respectively denote the event of selecting box A, B, C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box A is
Question:12(ii) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box B?
Answer:
Let R be event of drawing red marble.
Let respectivly denote event of selecting box A,B,C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box B is
Question:12(iii) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box C?
Answer:
Let R be event of drawing red marble.
Let respectivly denote event of selecting box A,B,C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box C is
Answer:
Let A,E1, E2 respectively denote the event that a person has a heart break, selected person followed the course of yoga and meditation , and the person adopted
the drug prescription.
the probability that the patient followed a course of meditation and yoga is
Answer:
Total number of determinant of second order with each element being 0 or 1 is
The values of determinant is positive in the following cases
Probability is
P(A fails) =
P(B fails alone) =
P(A and B fail) =
Evaluate the following probabilities
Answer:
Let event in which A fails and B fails be
P(A fails) =
P(B fails alone) =
P(A and B fail) =
Evaluate the following probabilities
Answer:
Let event in which A fails and B fails be
Answer:
Let E1 and E2 respectively denote the event that red ball is transfered from bag 1 to bag 2 and a black ball is transfered from bag 1 to bag2.
and
Let A be the event that ball drawn is red.
When a red ball is transfered from bag 1 to bag 2.
When a black ball is transfered from bag 1 to bag 2.
Question:17 If A and B are two events such that and then
Choose the correct answer of the following:
(A)
(B)
(C)
(D)
Answer:
A and B are two events such that and
Option A is correct.
As the name suggests NCERT solutions for Class 12 Maths chapter 13 miscellaneous exercise consist of different types of questions from all the previous exercises of the probability. This exercise is considered to be tough as compared to the previous exercises but it is not as important as previous exercises of this chapter for board exams. There are very few questions in board exams that are asked from miscellaneous exercises but it is very important for competitive exams. Students are advised to solve this exercise also to get command on the concept.
Also see-
Happy learning!!!
More than 95% of questions in the board's exam are not asked from miscellaneous exercises but it is very important for competitive exams.
Miscellaneous exercise is consists of different questions from all the topics of probability Class 12 Maths.
The probability of an impossible event is 0.
The probability of getting 0 when we roll a die is zero.
The probability of a number less than 7 when we roll a die is one.
The event of getting a number less than 7 when we roll a die is an example of a certain event.
The event of getting number 0 we roll a die is an example of an impossible event.
Here you can get NCERT Solutions.
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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:
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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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