RD SHARMA Solutions for Class 10 Maths Chapter 16 - Probability

Chapter 16 - Probability Exercise Ex. 16.1

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

(iv) a number lying between 2 and 6

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
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)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 15

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

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 black

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 white

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 spade

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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) 1

Question 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

 

 

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 coin

Solution 47

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

 

 

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 number

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 50

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

Solution 50

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
 
 
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
 
 
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability
 
 
Question 50(xvi)

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

2 will come up at least once

Solution 50(xvi)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 50(xvii)

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

2 will not come either time

Solution 50(xvii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 51

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

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

(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.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

Question 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

(iv) card  (v) diamond

Solution 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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) King

Solution 65

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

 

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 20

Solution 66

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 card

Solution 67

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 card

Solution 68

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 queen

Solution 69

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability


 

 

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - ProbabilityRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 3(i)

Three coins are tossed together. Find the probability of getting :Exactly two heads

Solution 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) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 3(ii)

Three coins are tossed together. Find the probability of getting :At most two heads

Solution 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) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

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) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 3(iv)

Three coins are tossed together. Find the probability of getting :No tails

Solution 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) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(i)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :

The sum of the two numbers that turn up is 8? 

Solution 53(i)

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 sum of two numbers which turn up is 8.

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

n(A) = 5

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 53(ii)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :

Of obtaining a total of 6? 

Solution 53(ii)

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 sum of two numbers which turn up is 6.

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

n(A) = 5

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(iii)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :Of obtaining a total of 10?

Solution 53(iii)

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 sum of two numbers which turn up is 10.

A = {(4,6),(6,4),(5,5)}

n(A) = 3

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(iv)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :Of obtaining the same number on both dice?

Solution 53(iv)

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 of obtaining the same number on both dice.

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

n(A) = 6

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(v)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that : Of obtaining a total more than 9?

Solution 53(v)

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 of obtaining a total more than 9.

A = {(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)}

n(A) = 6

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(vi)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :That the sum of the numbers appearing on the top of the dice is 13?

Solution 53(vi)

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 sum of the numbers appearing on the top of the dice is 13.

The maximum total of the numbers on the dice is 12.

Hence, n(A) = 0

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(vii)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :That the sum of the numbers appearing on the top of the dice is less than or equal to 12?

Solution 53(vii)

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 sum of the numbers appearing on the top of the dice is less than or equal to 12.

The maximum total of the numbers on the dice is 12.

Hence, n(A) = 36

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(viii)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :That the product of numbers appearing on the top of dice is less than 9.

Solution 53(viii)

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 product of numbers appearing on the top of the dice is less than 9.

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

 (2,1)(2,2),(2,3),(2,4), (3,1),(3,2),

 (4,1),(4,2),(5,1),(6,1)}

n(A) = 16

 

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(ix)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that :That the difference of the numbers appearing on the top of the two dice is 2.

Solution 53(ix)

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 difference of the numbers appearing on the top of the two dice is 2.

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

}

n(A) = 8

P(A) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Question 53(x)

A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that : 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) = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability 

Chapter 16 - Probability Exercise Ex. 16.2

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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?

 



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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?


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - ProbabilityJAB?
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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?

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Chapter 16 - Probability Exercise 16.35

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 1

n(E) = total numbers

       = 9

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

       = 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (b).

Question 2

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 2

n(E) = 9

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

       = 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (a).

Chapter 16 - Probability Exercise 16.36

Question 3

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 3

n(E) = 9

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

       = 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (a).

Question 4

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (c).

Question 5

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (b).

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 9

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 10

n(S) = 52

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

n(E) = 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (b).

Question 11

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

 

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

Question 12

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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) 0.95

Solution 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) 1.6

Solution 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 existent

Solution 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 16 - Probability Exercise 16.37

Question 16

The probability of an impossible event is

(a) 0

(b) 1

(c) 1/2

(d) non-existent

Solution 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?

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 18

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Chapter 16 - Probability Exercise 16.38

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 31

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (b).

 

Question 33

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

So, the correct option is (b).

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 35

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 36

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

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Chapter 16 - Probability Exercise 16.39

Question 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Probability