RD SHARMA SOLUTION CHAPTER- 13 Probability| CLASS 10TH MATHEMATICS-EDUGROWN

Chapter 13 – Probability Exercise Ex. 13.1

Question 1

Solution 1

Question 2

A die is thrown. Find the probability of getting:

(i) a prime number

(ii) 2 or 4

(iii) a multiple of 2 or 3

(iv) an even prime number

(v) a number greater than 5

(vi) a number lying between 2 and 6

(vii) A die is thrown. Find the probability of getting: a composite number.Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 6(xix)

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a king nor a queen.Solution 6(xix)

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

If the probability of winning a game is 0.3, what is the probability of loosing it?Solution 15

Question 16

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) red (ii) black or white (iii) not blackSolution 16

Question 17

A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) white (ii) red (iii) not black (iv) red or whiteSolution 17

Question 18

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red suit

(ii) a face card

(iii) a red face card

(iv) a queen of black suit

(v) a jack of hearts

(vi) a spadeSolution 18

Question 19(i)

Five cards-ten, jack, queen, king, and an ace of diamonds are shuffled face downwards. One card is picked at random.

(i) What is the probability that the card is a queen?


Solution 19(i)

Question 19(ii)

Five cards – ten, jack, queen, king, and an ace of diamonds are shuffled face downwards.  One card is picked at random.

If a king is drawn first and put aside, what is the probability that the second card picked up is the

(i)ace? (ii)king?Solution 19(ii)

Question 20

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) black?Solution 20

Question 21

Solution 21

Question 22

In A Class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixed  thoroughly. A child is asked to one card from the basket. What is the probability that the name written on the card is

(i) The name of a girl  

(ii) The name of a boySolution 22

Question 23

Solution 23

A coin has only two options-head and tail and both are equally likely events i.e. the probability of occurrence of both is same. Hence, a coin is a fair option to decide which team will choose ends in the game.Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Harpreet tosses two different coins simultaneously (say, one is of Re 1 and other of Rs 2). What is the probability that gets at least one head?Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Fill in the blanks:

(i) Probability of a sure event is ________.

(ii) Probability of an impossible event is _______.

(iii) The probability of an event (other than sure and impossible event) lies between ______.

(iv) Every elementary event associated to a random experiment has _______ probability.

(v) Probability of an event A + Probability of an event ‘not A’ = ___________.

(vi) Sum of the probabilities of each outcome in an experiment is ____________.Solution 41

(i) 1

(ii) 0

(iii) 0 and 1

(iv) equal

(v) 1

(vi) 1Question 42

Solution 42

Question 43

A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.Solution 43

Question 44

A box contains cards numbered 3,5,7,9,…,35,37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.Solution 44

Question 45

A group consists of 12 persons, of which 3 are extremely patient, 6 are extremely honest and the rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above would you prefer more?Solution 45

Question 46

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is,

(i) Not divisible by 3

(ii) A prime number greater than 7

(iii) Not a perfect square number.Solution 46

Question 47

A piggy bank contains hundred 50 paise coins, fifty Rs. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which falls out

(i) is a 50 paise win

(ii) is of value more than Rs. 1

(iii) is of value less than Rs. 5

(iv) is a Rs. 1 or Rs. 2 coinSolution 47

Question 48

A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is

(i) an odd number

(ii) a multiple of 5

(iii) a perfect square

(iv) an even prime numberSolution 48

Question 49

A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is

1. divisible 2 or 3
2. a prime number

Solution 49

Question 50

Solution 50

  Question 50(xvi)

In a simultaneous throw of a pair of dice, find the probability that:

2 will come up at least onceSolution 50(xvi)

Question 50(xvii)

In a simultaneous throw of a pair of dice, find the probability that:

2 will not come either timeSolution 50(xvii)

Question 51

What is the probability that an ordinary year has 53 Sundays?Solution 51

Question 52

Solution 52

Question 53

(viii) that the product of numbers appearing on the top of the dice is less than 9.

(ix) that the difference of the numbers appearing on the top of the two dice is 2.

(x) that the numbers obtained have a product less than 16.Solution 53

(x)

When a black die and a white die are thrown at the same time, the sample space is given by

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),

(2,1)(2,2),(2,3),(2,4),(2,5),(2,6),

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

n(S) = 36

Let A be the event that the numbers obtained have a product less than 16.

A = {{(1,1),(1,2),(1,3),(1,4),(1,5),

(1,6),(2,1)(2,2),(2,3),(2,4),(2,5),

(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),

(4,1),(4,2),(4,3), (5,1),(5,2),

(5,3),(6,1),(6,2)}}

n(A) = 25

P(A) =  Question 54

Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

Solution 60

Question 61

(iv) card  (v) diamondSolution 61

Question 62

Solution 62

Question 63

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.Solution 63

Question 64

A dice is rolled twice. Find the probability that

(i) 5 will not come up either time.

(ii) 5 will come up exactly once.Solution 64

Question 65

All the black face cards are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a

(i) Face card

(ii) Red card

(iii) Black card

(iv) KingSolution 65

Question 66

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is

(i) an odd number

(ii) a perfect square number

(iii) divisible by 5

(iv) a prime number less than 20Solution 66

Question 67

All kings and queens are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is

(i) a red face card

(ii) a black cardSolution 67

Question 68

All jacks, queens and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is

(i) a black face card

(ii) a red cardSolution 68

Question 69

Red queens and black jacks are removed from a pack of 52 playing  is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is

(i) a king

(ii) of red colour

(iii) a face card

(iv) a queenSolution 69

Question 70

In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 are blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure

1. square
2. green colour,
3. blue circle and
4. green square.

Solution 70

Question 71

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is

1. a red card
2. a face card and
3. a card of clubs.

Solution 71

Question 72

Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) different days? (iii) consecutive days?Solution 72

Question 3(i)

Three coins are tossed together. Find the probability of getting :Exactly two headsSolution 3(i)

Sample space when three coins are tossed together is

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

Let A be the event ofgetting exactly two heads.

A = {HHT, THH, HHT}

n (A) = 3

P(A) =  Question 3(ii)

Three coins are tossed together. Find the probability of getting :At most two headsSolution 3(ii)

Sample space when three coins are tossed together is

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

Let A be the event of getting at most two heads.

A = {TTT, HTT, THT, TTH, HHT, THH, HHT}

n (A) = 7

P(A) =  Question 3(iii)

Three coins are tossed together. Find the probability of getting :At least one head and one tail.Solution 3(iii)

Sample space when three coins are tossed together is

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

Let A be the event of getting at least one head and one tail.

A = {HHT, HTH, THH, HTT, THT, TTH }

n (A) = 6

P(A) =  Question 3(iv)

Three coins are tossed together. Find the probability of getting :No tailsSolution 3(iv)

Sample space when three coins are tossed together is

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

Let A be the event ofgetting no tails.

A = {HHH}

n (A) = 1

P(A) =  

Chapter 13 – Probability Exercise Ex. 13.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

A target shown in Fig. 16.11 consists of three concentric circles of radii 3, 7 and 9 cm respectively. A dart is thrown and lands on the target. What is the probability that the dart will land on the shaded region?

Solution 3

Assume first circle to be the circle with the smallest radius, that is 3. Similarly, second circle to be the circle with radius 7 and third circle to be the circle with radius 9.

Question 4

In Fig. 16.12, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

Solution 4

Question 5

In the fig., JKLM is a square with sides of length 6 units. Points A and B are the mid-points of sides KL and LM respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of JAB?
Solution 5

Question 6

In the fig., a square dart board is shown. The length of a side of the larger square is 1.5 times the length of a side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square?

Solution 6

Chapter 13 – Probability Exercise 13.35

Question 1

If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, then the probability that it is odd, is

Solution 1

n(E) = total numbers

       = 9

n(0) = odd numbers {1, 3, 5, 7, 9}

       = 5

So, the correct option is (b).Question 2

In Q. No. 1, the probability that the digit is even, is

Solution 2

n(E) = 9

n(4) = no. is even {2, 4, 6, 8}

       = 4

So, the correct option is (a).

Chapter 13 – Probability Exercise 13.36

Question 3

In Q. No. 1, the probability that the digit is a multiple of 3 is

Solution 3

n(E) = 9

n(A) = no. is multiple of 3 {3, 6, 9}

       = 3

So, the correct option is (a).Question 4

If three coins are tossed simultaneously, then the probability of getting at least two heads, is

Solution 4

3 coins are tossed simultaneously.

Hence sample space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Event (E) = at least two Heads

              = {HHH, HHT, HTH, THH}

n(s) = 8

n(E) = 4

So, the correct option is (c).Question 5

In a single throw of a die, the probability of getting a multiple of 3 is

Solution 5

sample space (s) = {1, 2, 3, 4, 5, 6}

n(s) = 6

Event (E) = getting a multiple of 3

              = {3, 6}

n(E) = 2

So, the correct option is (b).Question 6

Solution 6

Question 7

A bag contains three green marbles, four blue marbles, and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is

Solution 7

Question 8

A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9 The probability that the selected number is their average is

Solution 8

Question 9

The probability of throwing a number greater than 2 with a fair dice is

Solution 9

Sample space (S) = {1, 2, 3, 4, 5, 6}

n(S) = 6

Event (E) = getting number greater than 2

              = {3, 4, 5, 6}

n(E) = 4

So, the correct option is (c).Question 10

A card is accidently dropped from a pack of 52 playing cards. The probability that it is an ace is

Solution 10

n(S) = 52

no. of ace in a pack of 52 cards = 4

n(E) = 4

So, the correct option is (b).Question 11

A number is selected from numbers 1 to 25. The probability that it is prime is

Solution 11

n(S) = 25

Event (E) = prime numbers between 1 to 25

              = {2, 3, 5, 7, 11, 13, 17, 19, 23}

n(E) = 9

Note: The answer does not match the options in the question.Question 12

Which of the following cannot be the probability of an event?

Solution 12

We know probability P(E) of an event lies between 0 < P(E) < 1     ……(1)

(a), (c), (d) satisfies the (1) but (b) is a negative number. It can’t be the probability of an event.

So, the correct option is (b).Question 13

If P(E) = 0.05, then P(not E) =

(a) – 0.05

(b) 0.5

(c) 0.9

(d) 0.95Solution 13

We know

P(E) + P(not E) = 1

given P(E) = 0.05

so P(not E) = 1 – 0.05

                 = 0.95

So, the correct option is (d).Question 14

Which of the following cannot be the probability of occurrence of an event?

(a) 0.2

(b) 0.4

(c) 0.8

(d) 1.6Solution 14

We know 0 < P(E) < 1

(a), (b), (c) fullfill the condition. But (d) doesn’t 

Hence (d) is correct option.

So, the correct option is (d).Question 15

The probability of a certain event is

(a) 0

(b) 1

(c) 1/2

(d) no existentSolution 15

An event that is certain to occur is called Certain event.

Probability of certain event is 1.

Ex: If it is Monday, the probability that tomorrow is Tuesday is certain and therefore probability is 1.

So, the correct option is (b).

Chapter 13 – Probability Exercise 13.37

Question 16

The probability of an impossible event is

(a) 0

(b) 1

(c) 1/2

(d) non-existentSolution 16

Events that are not possible are impossible event.

Probability of impossible event is 0.

So, the correct option is (a).Question 17

Aarushi sold 100 lottery tickets in which 5 tickets carry prizes. If Priya purchased a ticket, what is the probability of Priya winning a prize?

Solution 17

Question 18

A number is selected from first 50 natural numbers. What is the probability that it is a multiple of 3 or 5 ?

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Chapter 13 – Probability Exercise 13.38

Question 28

Solution 28

Question 29

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3 the probability that |x| < 2 is

Solution 29

Sample space (s) = {-3, -2, -1, 0, 1, 2, 3}

n(s) = 7

Event (E) = |x| < 2

             = {-1, 0, 1}

n(E) = 3

So, the correct option is (c).Question 30

If a number x is chosen from the numbers 1, 2, 3, and a number y is selected from the number 1, 4, 9. Then, P(xy < 9)

Solution 30

Question 31

The probability that a non-leap year has 53 Sundays, is

Solution 31

There are 365 days in a non-leap year.

52 complete weeks and 1 spare day.

so This day can be any out of 7 day of week.

Hence n(s) = 7

Now, year already have 52 Sundays. so for a total of 53 Sundays in a calendar year, this spare day must be a Sunday.

Hence n(E) = 1

So, the correct option is (d).Question 32

In a single throw of a pair of dice, the probability of getting the sum a perfect sqaure is

Solution 32

We know on throwing a pair of die there are a total of 36 possible outcomes.

n(S) = sum is a perfect square

        = {(1, 3), (2, 2), (3, 1), (3, 6), (4, 5), (5, 4), (6, 3)}

n(E) = 7

So, the correct option is (b).Question 33

What is the probability that a non-leap year has 53 Sundays ?

Solution 33

There are 365 days in a non-leap year.

52 complete weeks and 1 spare day.

So this day can be any out of 7 day of a week.

Hence n(s) = 7

Now, a non-leap year already has 52 Sundays. So for a total of 53 Sundays in a calendar year, this spare day must be a Sunday.

Hence n(E) = 1

So, the correct option is (b).Question 34

Solution 34

Question 35

Two dice are rolled simultaneously. The probability that they show different faces is

Solution 35

Question 36

What is the probability that a leap year has 52 Mondays?

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Chapter 13 – Probability Exercise 13.39

Question 39

Solution 39

Question 40

Solution 40