NCERT Solutions for Maths Class 12 Exercise 13.3

# NCERT Solutions for Maths Class 12 Exercise 13.3

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 13.3.

You can download the PDF of NCERT Books Maths Chapter 10 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 13.3.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

NCERT Solutions for Maths Class 12 Exercise 13.1

NCERT Solutions for Maths Class 12 Exercise 13.2

## NCERT Solutions for Maths Class 12 Exercise 13.3

Maths Class 12 Ex 13.3 Question 1.

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?

Solution:

The urn contains 5 red and 5 black balls.
(i) Let a red ball is drawn.
Probability of drawing a red ball = 5/10 = ½
Now, two red balls are added to the urn.
Then, the urn contains 7 red and 5 black balls.
Now, the probability of drawing a red ball = 7/12
(ii) Let a black ball is drawn at first attempt.
Probability of drawing a black ball = 5/10 = ½
Next two black balls are added to the urn.
Now, urn contains 5 red and 7 black balls.
Probability of getting a red ball = 5/12
Then, the probability of drawing a second ball as red

= ½ × 7/12 + ½ × 5/12

= 7/24 + 5/24 = 12/24 = ½

Maths Class 12 Ex 13.3 Question 2.

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.

Solution:

Let A be the event that ball drawn is red and let E1 and E2 be the events that the ball drawn is from the first bag and second bag respectively.

P(E1) = ½, P(E2) = ½.
P(A|E1) = Probability of drawing a red ball from bag

Maths Class 12 Ex 13.3 Question 3.

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 a hostler?

Solution:

Let E1, E2 and A represents the following:
E1 = students residing in the hostel
E2 = day scholars (not residing in the hostel)
and A = students who attain grade A

Maths Class 12 Ex 13.3 Question 4.

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and ¼ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability ¼. What is the probability that the student knows the answer given that he answered it correctly?

Solution:

Let the event E1 = student knows the answer, E2 = he guesses the answer
P(E1) = 3/4, P(E2) = ¼
Let A be the event that answer is correct, if the student knows the answer.

The answer is correct. Therefore, P(A/E1) = 1

If he guesses the answer, therefore, P(A/E2) = ¼

Thus, the probability that a student knows the answer, given that answer is correct, is

Maths Class 12 Ex 13.3 Question 5.

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 (i.e. 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?

Solution:

Let E1 = The person selected is suffering from certain disease,
E2 = The person selected is not suffering from certain disease

A = The doctor diagnoses correctly

Maths Class 12 Ex 13.3 Question 6.

There are three coins. One is a two headed coin, 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 head, what is the probability that it was the two headed coin?

Solution:

Let E1, E2, E3 and A denote the following:
E1 = a two headed coin, E2 = a biased coin,
E3 = an unbiased coin, A = A head is shown

Maths Class 12 Ex 13.3 Question 7.

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

Solution:

Let E1 = the person selected is a scooter driver, E2 = the person selected is a car driver, E3 = the person selected is a truck driver and A = the person meets with an accident

Total number of drivers = 2000 + 4000 + 6000 = 12,000
Probability of selecting a scooter driver

Maths Class 12 Ex 13.3 Question 8.

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 it was produced by machine B?

Solution:

Let E1 and E2 be the events the percentage of production of items by machine A and machine B respectively.
Let A denotes defective item.
Machine A’s production of items = 60%
Probability of production of items by machine A

Maths Class 12 Ex 13.3 Question 9.

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.

Solution:

Given: P(G1) = 0.6, P(G2) = 0.4
Let P represents the launching of new product, then P(P|G1) = 0.7 and P(P|G2) = 0.3

Maths Class 12 Ex 13.3 Question 10.

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?

Solution:

Maths Class 12 Ex 13.3 Question 11.

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, whereas 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 it was produced by A?

Solution:

Let E1, E2, E3 and A be the events defined as follows:
E1 = the item is manufactured by the operator A
E2 = the item is manufactured by the operator B
E3 = the item is manufactured by the operator C
and A = the item is defective

Maths Class 12 Ex 13.3 Question 12.

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?

Solution:

Let E1 = Event that lost card is diamond,
E2 = Event that lost card is not diamond.
There are 13 diamond cards, out of a pack or 52 cards.

Maths Class 12 Ex 13.3 Question 13.

Probability that A speaks truth is 4/5. A coin is tossed. A reports that a head appears. The probability that actually there was head is:
(A) 4/5
(B) ½
(C) 1/5
(D) 2/5

Solution:

(A) Let A be the event that the man reports that head occurs in tossing a coin and let E1 be the event that head occurs and E2 be the event head does not occurs.

Maths Class 12 Ex 13.3 Question 14.

If A and B are two events such that A B and P(B) ≠ 0, then which of the following is correct:
(A) P(A|B) = P(B)/P(A)
(B) P(A|B) < P(A)
(C) P(A|B) ≥ P(A)
(D) None of these

Solution:

(C) A B implies that A∩B = A and P(B) ≠ 0