NCERT Solutions for Class 12 Maths Maths Part-2 Chapter 13

Probability Class 12

Chapter 13 Probability Exercise 13.1, 13.2, 13.3, 13.4, 13.5, miscellaneous Solutions

<< Previous Chapter 12 : Linear Programming

Exercise 13.1 : Solutions of Questions on Page Number : 538

Q1 :  

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∠© F) = 0.2, find P (E|F) and P(F|E).


Answer :

It is given that P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.2

Answer needs Correction? Click Here

Q2 :  

Compute P(A|B), if P(B) = 0.5 and P (A ∠© B) = 0.32


Answer :

It is given that P(B) = 0.5 and P(A ∩ B) = 0.32

Answer needs Correction? Click Here

Q3 :  

If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find

(i) P(A ∠© B) (ii) P(A|B) (iii) P(A ∠ª B)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Evaluate P (A ∪ B), if 2P (A) = P (B) =and P(A|B) =


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

If P(A), P(B) =and P(A ∪ B) =, find

(i) P(A ∩ B) (ii) P(A|B) (iii) P(B|A)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

A coin is tossed three times, where

(i) E: head on third toss, F: heads on first two tosses

(ii) E: at least two heads, F: at most two heads

(iii) E: at most two tails, F: at least one tail


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Two coins are tossed once, where

(i) E: tail appears on one coin, F: one coin shows head

(ii) E: not tail appears, F: no head appears


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

A die is thrown three times,

E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Mother, father and son line up at random for a family picture

E: son on one end, F: father in middle


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

A black and a red dice are rolled.

(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}

Find

(i) P (E|F) and P (F|E) (ii) P (E|G) and P (G|E)

(ii) P ((E ∠ª F)|G) and P ((E ∠© G)|G)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

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. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

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'.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

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. Find the conditional probability of the event 'the coin shows a tail', given that 'at least one die shows a 3'.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

If

(A) 0 (B)

(C) not defined (D) 1


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

If A and B are events such that P (A|B) = P(B|A), then

(A) A ⊂ B but A ≠ B (B) A = B

(C) A ∠© B = Φ (D) P(A) = P(B)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Exercise 13.2 : Solutions of Questions on Page Number : 546

Q1 :  

If, find P (A ∩ B) if A and B are independent events.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

A fair coin and an unbiased die are tossed. Let A be the event 'head appears on the coin' and B be the event '3 on the die'. Check whether A and B are independent events or not.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, 'the number is even,' and B be the event, 'the number is red'. Are A and B independent?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

Let E and F be events with. Are E and F independent?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

Given that the events A and B are such thatand P (B) = p. Find p if they are (i) mutually exclusive (ii) independent.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find

(i) P (A ∠© B) (ii) P (A ∠ª B)

(iii) P (A|B) (iv) P (B|A)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

If A and B are two events such that, find P (not A and not B).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Events A and B are such that . State whether A and B are independent?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find

(i) P (A and B) (ii) P (A and not B)

(iii) P (A or B) (iv) P (neither A nor B)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

A die is tossed thrice. Find the probability of getting an odd number at least once.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that

(i) both balls are red.

(ii) first ball is black and second is red.

(iii) one of them is black and other is red.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

Probability of solving specific problem independently by A and B arerespectively. If both try to solve the problem independently, find the probability that

(i) the problem is solved (ii) exactly one of them solves the problem.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?

(i) E: 'the card drawn is a spade'

F: 'the card drawn is an ace'

(ii) E: 'the card drawn is black'

F: 'the card drawn is a king'

(iii) E: 'the card drawn is a king or queen'

F: 'the card drawn is a queen or jack'


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English news papers. A student is selected at random.

(a) Find the probability that she reads neither Hindi nor English news papers.

(b) If she reads Hindi news paper, find the probability that she reads English news paper.

(c) If she reads English news paper, find the probability that she reads Hindi news paper.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

(A) 0 (B) (C) (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

Two events A and B will be independent, if

(A) A and B are mutually exclusive

(B)

(C) P(A) = P(B)

(D) P(A) + P(B) = 1


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Exercise 13.3 : Solutions of Questions on Page Number : 555

Q1 :  

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability What is the probability that the student knows the answer given that he answered it correctly?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (that is, if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

There are three coins. One is two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that was produced by machine B?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that was produced by A?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Probability that A speaks truth is. A coin is tossed. A reports that a head appears. The probability that actually there was head is

A.

B.

C.

D.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?

A.

B.

C.

D. None of these


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Exercise 13.4 : Solutions of Questions on Page Number : 569

Q1 :  

State which of the following are not the probability distributions of a random variable. Give reasons for your answer.

(i)

X

0

1

2

P (X)

0.4

0.4

0.2

(ii)

X

0

1

2

3

4

P (X)

0.1

0.5

0.2

- 0.1

0.3

(iii)

Y

- 1

0

1

P (Y)

0.6

0.1

0.2


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represents the number of black balls. What are the possible values of X? Is X a random variable?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Let X represents the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Find the probability distribution of

(i) number of heads in two tosses of a coin

(ii) number of tails in the simultaneous tosses of three coins

(iii) number of heads in four tosses of a coin


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as

(i) number greater than 4

(ii) six appears on at least one die


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

A random variable X has the following probability distribution.

X

0

1

2

3

4

5

6

7

P (X)

0

k

2k

2k

3k

k2

2k2

7k2 + k

Determine

(i) k

(ii) P (X < 3)

(iii) P (X > 6)

(iv) P (0 < X < 3)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

The random variable X has probability distribution P(X) of the following form, where k is some number:

(a) Determine the value of k.

(b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

Find the mean number of heads in three tosses of a fair coin.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Let X denotes the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

(A) 1 (B) 2 (C) 5 (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is

(A) (B) (C) (D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Exercise 13.5 : Solutions of Questions on Page Number : 576

Q1 :  

A die is thrown 6 times. If 'getting an odd number' is a success, what is the probability of

(i) 5 successes? (ii) at least 5 successes?

(iii) at most 5 successes?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that

(i) all the five cards are spades?

(ii) only 3 cards are spades?

(iii) none is a spade?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs

(i) none

(ii) not more than one

(iii) more than one

(iv) at least one

will fuse after 150 days of use.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true'; if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

Suppose X has a binomial distribution. Show that X = 3 is the most likely outcome.

(Hint: P(X = 3) is the maximum among all P (xi), xi = 0, 1, 2, 3, 4, 5, 6)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

Find the probability of getting 5 exactly twice in 7 throws of a die.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Find the probability of throwing at most 2 sixes in 6 throws of a single die.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

(A) 10 - 1

(B)

(C)

(D)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

The probability that a student is not a swimmer is. Then the probability that out of five students, four are swimmers is

(A) (B)

(C) (D) None of these


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Exercise Miscellaneous : Solutions of Questions on Page Number : 582

Q1 :  

A and B are two events such that P (A) ≠ 0. Find P (B|A), if

(i) A is a subset of B (ii) A ∠© B = Φ


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

A couple has two children,

(i) Find the probability that both children are males, if it is known that at least one of the children is male.

(ii) Find the probability that both children are females, if it is known that the elder child is a female.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

Suppose that 5% of men and 0.25% of women have grey hair. A haired person is selected at random. What is the probability of this person being male?

Assume that there are equal number of males and females.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that

(i) all will bear 'X' mark.

(ii) not more than 2 will bear 'Y' mark.

(iii) at least one ball will bear 'Y' mark

(iv) the number of balls with 'X' mark and 'Y' mark will be equal.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is. What is the probability that he will knock down fewer than 2 hurdles?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q7 :  

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q8 :  

If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q9 :  

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q10 :  

How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q11 :  

In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins/loses.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q12 :  

Suppose we have four boxes. A, B, C and D containing coloured marbles as given below:

Box

Marble colour

Red

White

Black

A

1

6

3

B

6

2

2

C

8

1

1

D

0

6

4

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?, box B?, box C?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q13 :  

Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q14 :  

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability).


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q15 :  

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known:

P(A fails) = 0.2

P(B fails alone) = 0.15

P(A and B fail) = 0.15

Evaluate the following probabilities

(i) P(A fails| B has failed) (ii) P(A fails alone)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q16 :  

Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q17 :  

If A and B are two events such that P (A) ≠ 0 and P(B|A) = 1, then.

(A) A ⊂ B

(B) B ⊂ A

(C) B = Φ

(D) A = Φ


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q18 :  

If P (A|B) > P (A), then which of the following is correct:

(A) P (B|A) < P (B) (B) P (A ∠© B) < P (A).P (B)

(C) P (B|A) > P (B) (D) P (B|A) = P (B)


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q19 :  

If A and B are any two events such that P (A) + P (B) - P (A and B) = P (A), then

(A) P (B|A) = 1 (B) P (A|B) = 1

(C) P (B|A) = 0 (D) P (A|B) = 0


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 12 : Linear Programming

Maths Part-2 - Maths : CBSE NCERT Exercise Solutions for Class 12th for Probability ( Exercise 13.1, 13.2, 13.3, 13.4, 13.5, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles
Exercise 13.1
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Exercise 13.2
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Exercise 13.3
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Exercise 13.4
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Exercise 13.5
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Exercise Miscellaneous
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19