Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 12 - Introduction to probability theory [Latest edition]

#### Chapters ## Chapter 12: Introduction to probability theory

Exercise 12.1Exercise 12.2Exercise 12.3Exercise 12.4Exercise 12.5
Exercise 12.1 [Pages 246 - 247]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 12 Introduction to probability theoryExercise 12.1 [Pages 246 - 247]

Exercise 12.1 | Q 1. (i) | Page 246

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.

P(A) = 0.15, P(B) = 0.30, P(C) = 0.43, P(D)= 0.12

Exercise 12.1 | Q 1. (ii) | Page 246

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.

P(A) = 0.22, P(B) = 0.38, P(C) = 0.16, P(D) = 0.34

Exercise 12.1 | Q 1. (iii) | Page 246

An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.

P(A) = 2/5, P(B) = 3/5, P(C) = - 1/5, P(D) = 1/5

Exercise 12.1 | Q 2. (i) | Page 246

If two coins are tossed simultaneously, then find the probability of getting one head and one tail

Exercise 12.1 | Q 2. (ii) | Page 246

If two coins are tossed simultaneously, then find the probability of getting atmost two tails

Exercise 12.1 | Q 3. (i) | Page 246

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that one is a mango and the other is an apple

Exercise 12.1 | Q 3. (ii) | Page 246

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that both are of the same variety

Exercise 12.1 | Q 4. (i) | Page 247

What is the chance that non-leap year

Exercise 12.1 | Q 4. (ii) | Page 247

What is the chance that leap year should have fifty three Sundays?

Exercise 12.1 | Q 5. (i) | Page 247

Eight coins are tossed once, find the probability of getting exactly two tails

Exercise 12.1 | Q 5. (ii) | Page 247

Eight coins are tossed once, find the probability of getting atleast two tails

Exercise 12.1 | Q 5. (iii) | Page 247

Eight coins are tossed once, find the probability of getting atmost two tails

Exercise 12.1 | Q 6 | Page 247

An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?

Exercise 12.1 | Q 7. (i) | Page 247

A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that all are red

Exercise 12.1 | Q 7. (ii) | Page 247

A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that one red and 2 black

Exercise 12.1 | Q 8. (i) | Page 247

A single card is drawn from a pack of 52 cards. What is the probability that the card is an ace or a king

Exercise 12.1 | Q 8. (ii) | Page 247

A single card is drawn from a pack of 52 cards. What is the probability that the card will be 6 or smaller

Exercise 12.1 | Q 8. (iii) | Page 247

A single card is drawn from a pack of 52 cards. What is the probability that the card is either a queen or 9?

Exercise 12.1 | Q 9 | Page 247

A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

Exercise 12.1 | Q 10. (i) | Page 247

The odds that the event A occurs is 5 to 7, find P(A)

Exercise 12.1 | Q 10. (ii) | Page 247

Suppose P(B) = 2/5. Express the odds event B occurs

Exercise 12.2 [Page 250]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 12 Introduction to probability theoryExercise 12.2 [Page 250]

Exercise 12.2 | Q 1. (i) | Page 250

If A and B are mutually exclusive events P(A) = 3/8 and P(B) = 1/8, then find "P"(bar"A")

Exercise 12.2 | Q 1. (ii) | Page 250

If A and B are mutually exclusive events P(A) = 3/8 and P(B) = 1/8, then find "P"("A" ∪ "B")

Exercise 12.2 | Q 1. (iii) | Page 250

If A and B are mutually exclusive events P(A) = 3/8 and P(B) = 1/8, then find "P"(bar"A" ∩ "B")

Exercise 12.2 | Q 1. (iv) | Page 250

If A and B are mutually exclusive events P(A) = 3/8 and P(B) = 1/8, then find "P"(bar"A" ∪ bar"B")

Exercise 12.2 | Q 2. (i) | Page 250

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only B)

Exercise 12.2 | Q 2. (ii) | Page 250

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find "P"(bar"B")

Exercise 12.2 | Q 2. (iii) | Page 250

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15 Find P(only A)

Exercise 12.2 | Q 3 | Page 250

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event, ‘second
die shows 5’. Find P(A ∪ B)

Exercise 12.2 | Q 4. (i) | Page 250

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of P(A ∪ B)

Exercise 12.2 | Q 4. (ii) | Page 250

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of "P"("A" ∩ bar"B")

Exercise 12.2 | Q 4. (iii) | Page 250

The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of "P"(bar"A" ∩ "B")

Exercise 12.2 | Q 5. (i) | Page 250

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that a fire engine is available when needed?

Exercise 12.2 | Q 5. (ii) | Page 250

A town has 2 fire engines operating independently. The probability that a fire engine is available when needed is 0.96. What is the probability that neither is available when needed?

Exercise 12.2 | Q 6. (i) | Page 250

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get at least one of the two awards

Exercise 12.2 | Q 6. (ii) | Page 250

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that it will get only one of the awards

Exercise 12.3 [Pages 258 - 259]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 12 Introduction to probability theoryExercise 12.3 [Pages 258 - 259]

Exercise 12.3 | Q 1 | Page 258

Can two events be mutually exclusive and independent simultaneously?

Exercise 12.3 | Q 2 | Page 258

If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent

Exercise 12.3 | Q 3 | Page 258

If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)

Exercise 12.3 | Q 4 | Page 258

If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A ∪ B)

Exercise 12.3 | Q 5 | Page 258

If for two events A and B, P(A) = 3/4, P(B) = 2/5  and A ∪ B = S (sample space), find the conditional probability P(A/B)

Exercise 12.3 | Q 6. (i) | Page 259

A problem in Mathematics is given to three students whose chances of solving it are 1/3, 1/4 and 1/5. What is the probability that the problem is solved?

Exercise 12.3 | Q 6. (ii) | Page 259

A problem in Mathematics is given to three students whose chances of solving it are 1/3, 1/4 and 1/5. What is the probability that exactly one of them will solve it?

Exercise 12.3 | Q 7. (i) | Page 259

The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If the oil had to be changed, what is the probability that a new oil filter is needed?

Exercise 12.3 | Q 7. (ii) | Page 259

The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If a new oil filter is needed, what is the probability that the oil has to be changed?

Exercise 12.3 | Q 8. (i) | Page 259

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are white

Exercise 12.3 | Q 8. (ii) | Page 259

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are black

Exercise 12.3 | Q 8. (iii) | Page 259

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black

Exercise 12.3 | Q 9 | Page 259

Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

Exercise 12.3 | Q 10. (i) | Page 259

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are mutually exclusive

Exercise 12.3 | Q 10. (ii) | Page 259

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events

Exercise 12.3 | Q 10. (iii) | Page 259

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4

Exercise 12.3 | Q 10. (iv) | Page 259

Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5

Exercise 12.3 | Q 11. (i) | Page 259

A year is selected at random. What is the probability that it contains 53 Sundays

Exercise 12.3 | Q 11. (ii) | Page 259

A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays

Exercise 12.3 | Q 12 | Page 259

Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?

Exercise 12.4 [Pages 264 - 265]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 12 Introduction to probability theoryExercise 12.4 [Pages 264 - 265]

Exercise 12.4 | Q 1 | Page 264

A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

Exercise 12.4 | Q 2. (i) | Page 264

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it. find the probability that the ball is black

Exercise 12.4 | Q 2. (ii) | Page 264

There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it. if the ball is black, what is the probability that it is from the first urn?

Exercise 12.4 | Q 3. (i) | Page 264

A firm manufactures PVC pipes in three plants viz, X, Y and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production, find the probability that the selected pipe is a defective one

Exercise 12.4 | Q 3. (ii) | Page 264

A firm manufactures PVC pipes in three plants viz, X, Y and Z. The daily production volumes from the three firms X, Y and Z are respectively 2000 units, 3000 units and 5000 units. It is known from the past experience that 3% of the output from plant X, 4% from plant Y and 2% from plant Z are defective. A pipe is selected at random from a day’s total production, if the selected pipe is a defective, then what is the probability that it was produced by plant Y?

Exercise 12.4 | Q 4 | Page 265

The chances of A, B and C becoming manager of a certain company are 5 : 3 : 2. The probabilities that the office canteen will be improved if A, B, and C become managers are 0.4, 0.5 and 0.3 respectively. If the office canteen has been improved, what is the probability that B was appointed as the manager?

Exercise 12.4 | Q 5. (i) | Page 265

An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television, 30% of the time the husband is watching the television. Find the probability that the husband is watching the television during the prime time of television

Exercise 12.4 | Q 5. (ii) | Page 265

An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television, 30% of the time the husband is watching the television. Find the probability that if the husband is watching the television, the wife is also watching the television

Exercise 12.5 [Pages 265 - 267]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 12 Introduction to probability theoryExercise 12.5 [Pages 265 - 267]

#### MCQ

Exercise 12.5 | Q 1 | Page 265

Choose the correct alternative:

Four persons are selected at random from a group of 3 men, 2 women and 4 children. The probability that exactly two of them are children is

• 3/4

• 10/23

• 1/2

• 10/21

Exercise 12.5 | Q 2 | Page 265

Choose the correct alternative:

A number is selected from the set {1, 2, 3, ..., 20). The probability that the selected number is divisible by 3 or 4 is

• 2/5

• 1/8

• 1/2

• 2/3

Exercise 12.5 | Q 3 | Page 265

Choose the correct alternative:

A, B, and C try to hit a target simultaneously but independently. Their respective probabilities of hitting the target are 3/4, 1/2, 5/8. The probability that the target is hit by A or B but not by C is

• 21/64

• 7/32

• 9/64

• 7/8

Exercise 12.5 | Q 4 | Page 265

Choose the correct alternative:

If A and B are any two events, then the probability that exactly one of them occur is

• "P"("A" ∪ bar"B") + P(bar"A" ∪ "B")

• "P"("A" ∩ bar"B") + P(bar"A" ∩ "B")

• P(A) + P(B) – P(A ∩ B)

• P(A) + P(B) + 2P(A ∩ B)

Exercise 12.5 | Q 5 | Page 265

Choose the correct alternative:

Let A and B be two events such that "P"(bar ("A" ∪ "B")) = 1/6, "P"("A" ∩ "B") = 1/4 and "P"(bar"A") = 1/4. Then the events A and B are

• Equally likely but not independent

• Independent but not equally likely

• Independent and equally likely

• Mutually inclusive and dependent

Exercise 12.5 | Q 6 | Page 265

Choose the correct alternative:

Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

• 19/33

• 17/33

• 23/33

• 13/33

Exercise 12.5 | Q 7 | Page 266

Choose the correct alternative:

A man has 3 fifty rupee notes, 4 hundred rupees notes and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

• 1 : 12

• 12 : 1

• 13 : 1

• 1 : 13

Exercise 12.5 | Q 8 | Page 266

Choose the correct alternative:

A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is

• 7/45

• 17/90

• 29/90

• 19/90

Exercise 12.5 | Q 9 | Page 266

Choose the correct alternative:

A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is non zero will be

• 3/16

• 3/8

• 1/4

• 5/8

Exercise 12.5 | Q 10 | Page 266

Choose the correct alternative:

A bag contains 5 white and 3 black balls. Five balls are drawn successively without replacement. The probability that they are alternately of different colours is

• 3/14

• 5/14

• 1/14

• 9/14

Exercise 12.5 | Q 11 | Page 266

Choose the correct alternative:

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

• "P"("A"/"B") ("P"("A"))/("P"("B"))

• "P"("A"/"B") < "P"("A")

• "P"("A"/"B") ≥ "P"("A")

• "P"("A"/"B") > "P"("B")

Exercise 12.5 | Q 12 | Page 266

Choose the correct alternative:

A bag contains 6 green, 2 white, and 7 black balls. If two balls are drawn simultaneously, then the probability that both are different colours is

• 68/105

• 71/105

• 64/105

• 73/105

Exercise 12.5 | Q 13 | Page 266

Choose the correct alternative:

If X and Y be two events such that P(X/Y) = 1/2, P(Y/X) = 1/3 and P(X ∩ Y) = 1/6, then

• 1/3

• 2/5

• 1/6

• 2/3

Exercise 12.5 | Q 14 | Page 266

Choose the correct alternative:

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. The probability that the second ball drawn is red will be

• 5/12

• 1/2

• 7/12

• 1/4

Exercise 12.5 | Q 15 | Page 266

Choose the correct alternative:

A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies ((x  - 10)(x - 50))/(x - 30) ≥ 0, then P(A) is

• 0.20

• 0.51

• 0.71

• 0.70

Exercise 12.5 | Q 16 | Page 267

Choose the correct alternative:

If two events A and B are independent such that P(A) = 0.35 and P(A ∪ B) = 0.6, then P(B) is

• 5/13

• 1/13

• 4/13

• 7/13

Exercise 12.5 | Q 17 | Page 267

Choose the correct alternative:

If two events A and B are such that "P"(bar"A") = 3/10 and "P"("A" ∩ bar"B") = 1/2 then P(A ∩ B) is

• 1/2

• 1/3

• 1/4

• 1/5

Exercise 12.5 | Q 18 | Page 267

Choose the correct alternative:

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then "P"(bar"A" ∩ "B") is

• 0.96

• 0.24

• 0.56

• 0.66

Exercise 12.5 | Q 19 | Page 267

Choose the correct alternative:

There are three events A, B and C of which one and only one can happen. If the odds are 7 to 4 against A and 5 to 3 against B, then odds against C is

• 23 : 65

• 65 : 23

• 23 : 88

• 88 : 23

Exercise 12.5 | Q 20 | Page 267

Choose the correct alternative:

If a and b are chosen randomly from the set {1, 2, 3, 4} with replacement, then the probability of the real roots of the equation x2 + ax + b = 0 is

• 3/16

• 5/16

• 7/16

• 11/16

Exercise 12.5 | Q 21 | Page 267

Choose the correct alternative:

It is given that the events A and B are such that P(A) = 1/4, P(A/B) = 1/2 and P(B/A) = 2/3. Then P(B) is

• 1/6

• 1/3

• 2/3

• 1/2

Exercise 12.5 | Q 22 | Page 267

Choose the correct alternative:

In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

• 2/11

• 3/11

• 5/11

• 7/11

Exercise 12.5 | Q 23 | Page 267

Choose the correct alternative:

Ten coins are tossed. The probability of getting at least 8 heads is

• 7/64

• 7/32

• 7/16

• 7/128

Exercise 12.5 | Q 24 | Page 267

Choose the correct alternative:

The probability of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18. The probability that neither A nor B occurs is

• 0.1

• 0.72

• 0.42

• 0.28

Exercise 12.5 | Q 25 | Page 267

Choose the correct alternative:

If m is a number such that m ≤ 5, then the probability that quadratic equation 2x2 + 2mx + m + 1 = 0 has real roots is

• 1/5

• 2/5

• 3/5

• 4/5`

## Chapter 12: Introduction to probability theory

Exercise 12.1Exercise 12.2Exercise 12.3Exercise 12.4Exercise 12.5 ## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 12 - Introduction to probability theory

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Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 12 Introduction to probability theory are Some Basic Theorems on Probability, Conditional Probability, Total Probability of an Event, Bayes’ Theorem, Introduction to Probability Theory, Basic Definitions, Finite Sample Space, Probability.

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