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NCERT Solutions for Exercise 13.2 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. Most of the questions in NCERT solutions for exercise 13.2 Class 12 Maths chapter 13 deal with multiplication theorem on probability, independent events, and its property. This NCERT book exercise is very important from the board's exam point of view as one question is generally asked from this exercise. There are 7 examples given before this exercise which you should try to solve before solving the exercises questions. You can take help from exercise 13.2 Class 12 Maths solutions if you are stuck while solving these NCERT problems. These Class 12 Maths chapter 13 exercise 13.2 solutions are created by the subject matter experts who know how best to answer in the board exams.
12th class Maths exercise 13.2 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.
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Question:1 If and find if and are independent events.
Answer:
and
Given : and are independent events.
So we have,
Answer:
Two cards are drawn at random and without replacement from a pack of 52 playing cards.
There are 26 black cards in a pack of 52.
Let be the probability that first cards is black.
Then, we have
Let be the probability that second cards is black.
Then, we have
The probability that both the cards are black
Answer:
Total oranges = 15
Good oranges = 12
Bad oranges = 3
Let be the probability that first orange is good.
The, we have
Let be the probability that second orange is good.
Let be the probability that third orange is good.
The probability that a box will be approved for sale
Answer:
A fair coin and an unbiased die are tossed,then total outputs are:
A is the event ‘head appears on the coin’ .
Total outcomes of A are :
B is the event ‘3 on the die’.
Total outcomes of B are :
Also,
Hence, A and B are independent events.
Answer:
Total outcomes .
is the event, ‘the number is even,’
Outcomes of A
is the event, ‘the number is red’.
Outcomes of B
Also,
Thus, both the events A and B are not independent.
Question:6 Let and be events with and Are E and F independent?
Answer:
Given :
and
For events E and F to be independent , we need
Hence, E and F are not indepent events.
Question:7 Given that the events and are such that and Find if they are
(i) mutually exclusive
Answer:
Given,
Also, A and B are mutually exclusive means .
Question:7 Given that the events and are such that and Find p if they are
(ii) independent
Answer:
Given,
Also, A and B are independent events means
. Also
Question:8 Let A and B be independent events with and Find
(i)
Answer:
and
Given : A and B be independent events
So, we have
Question:8 Let and be independent events with and Find
(ii)
Answer:
and
Given : A and B be independent events
So, we have
We have,
Question:8 Let and be independent events with and Find
(iii)
Answer:
and
Given : A and B be independent events
So, we have
Question:8 Let A and B be independent events with and Find
(iv)
Answer:
and
Given : A and B be independent events
So, we have
Question:9 If and are two events such that and find
Answer:
If and are two events such that and
use,
Question:10 Events A and B are such that and State whether and are independent ?
Answer:
If and are two events such that and
As we can see
Hence, A and B are not independent.
Question:11 Given two independent events and such that Find
(i)
Answer:
Given two independent events and .
Also , we know
Question:11 Given two independent events A and B such that Find
(ii)
Answer:
Given two independent events and .
Question:12 A die is tossed thrice. Find the probability of getting an odd number at least once.
Answer:
A die is tossed thrice.
Outcomes
Odd numbers
The probability of getting an odd number at first throw
The probability of getting an even number
Probability of getting even number three times
The probability of getting an odd number at least once = 1 - the probability of getting an odd number in none of throw
= 1 - probability of getting even number three times
(i) both balls are red.
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
The probability of getting a red ball in first draw
The ball is repleced after drawing first ball.
The probability of getting a red ball in second draw
the probability that both balls are red
(ii) first ball is black and second is red.
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
The probability of getting a black ball in the first draw
The ball is replaced after drawing the first ball.
The probability of getting a red ball in the second draw
the probability that the first ball is black and the second is red
(iii) one of them is black and other is red.
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
Let the first ball is black and the second ball is red.
The probability of getting a black ball in the first draw
The ball is replaced after drawing the first ball.
The probability of getting a red ball in the second draw
the probability that the first ball is black and the second is red
Let the first ball is red and the second ball is black.
The probability of getting a red ball in the first draw
The probability of getting a black ball in the second draw
the probability that the first ball is red and the second is black
Thus,
The probability that one of them is black and the other is red = the probability that the first ball is black and the second is red + the probability that the first ball is red and the second is black
(i) the problem is solved
Answer:
and
Since, problem is solved independently by A and B,
probability that the problem is solved
(ii) exactly one of them solves the problem
Answer:
and
,
,
probability that exactly one of them solves the problem
probability that exactly one of them solves the problem
(i) E : ‘the card drawn is a spade’
F : ‘the card drawn is an ace’
Answer:
One card is drawn at random from a well shuffled deck of cards
Total ace = 4
total spades =13
E : ‘the card drawn is a spade
F : ‘the card drawn is an ace’
a card which is spade and ace = 1
Hence, E and F are indepentdent events .
(ii) E : ‘the card drawn is
F : ‘the card drawn is a king’
Answer:
One card is drawn at random from a well shuffled deck of cards
Total black card = 26
total king =4
E : ‘the card drawn is black’
F : ‘the card drawn is a king’
a card which is black and king = 2
Hence, E and F are indepentdent events .
(iii) E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’.
Answer:
One card is drawn at random from a well shuffled deck of cards
Total king or queen = 8
total queen or jack = 8
E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’.
a card which is queen = 4
Hence, E and F are not indepentdent events
(a) Find the probability that she reads neither Hindi nor English newspapers
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
the probability that she reads neither Hindi nor English newspapers
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
The probability that she reads English newspape if she reads Hindi newspaper
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper.
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
the probability that she reads Hindi newspaper if she reads English newspaper
Question:17 The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
(A)
(B)
(C)
(D)
Answer:
when a pair of dice is rolled, total outcomes
Even prime number
The probability of obtaining an even prime number on each die
Option D is correct.
Question:18 Two events A and B will be independent, if
(A) and are mutually exclusive
(B)
(C)
(D)
Answer:
Two events A and B will be independent, if
Or
Option B is correct.
Class 12 Maths chapter 13 exercise 13.2 solutions are consist of questions related to multiplication theorem on probability. There are 7 examples given before the NCERT syllabus exercise questions. You can solve them before solving the NCERT problems. There are 18 questions questions given in this exercise which you can solve. All these questions are solved in NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2 in a detailed manner. You can go through these solutions for reference.
Also Read| Probability Class 12th Notes
You can quickly revise the important concepts before the final exam.
Happy learning!!!
There are 18 questions in NCERT Class 12 Maths chapter 13 exercise 13.2.
If the occurrence of one event doesn’t affect the probability of the other event such events are called independent events.
The probability of getting a tail is 0.5 when we toss a fair coin.
You will get NCERT Exemplar Solutions for Class 12 Maths Probability by clicking on the given link.
An event is called an impossible event if the number of favorable outcomes is zero.
The probability of an impossible event is zero.
Click here to get NCERT Solutions for Class 12 Maths for other subjects.
The probability of getting head of this biased coin is 0.53.
Hello,
Yes, you can give improvement exams for 2-3 subjects in CBSE (Central Board of Secondary Education). CBSE allows students who have appeared for their Class 12 board exams to improve their scores by re-appearing for exams in up to five subjects the following year.
Hope this helps,
Thank you
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