RD SHARMA Solutions for Class 10 Maths Chapter 16 - Probability
Chapter 16 - Probability Exercise Ex. 16.1
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
(iv) a number lying between 2 and 6
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 black
Solution 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 white
Solution 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 spade
Solution 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
Solution 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) 1
Question 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 coin
Solution 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 number
Solution 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
- divisible 2 or 3
- 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 once
Solution 50(xvi)
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)
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
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) diamond
Solution 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) King
Solution 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 20
Solution 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 card
Solution 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 card
Solution 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 queen
Solution 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
- square
- green colour,
- blue circle and
- 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
- a red card
- a face card and
- 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 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)
= 
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)
= 
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 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)
= 
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)
= 
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)
=
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)
= 
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)
= 
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)
=
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)
= 
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)
= 
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)
= 
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)
= 
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)
= 
Chapter 16 - Probability Exercise Ex. 16.2
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 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
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 16 - Probability Exercise 16.36
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) 0.95
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?
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 16 - Probability Exercise 16.38
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 16 - Probability Exercise 16.39
Question 39
Solution 39
Question 40
Solution 40
Other Chapters for CBSE Class 10 Mathematics
Chapter 1- Real Numbers Chapter 2- Polynomials Chapter 3- Pairs of Linear Equations in Two Variables Chapter 4- Quadratic Equations Chapter 5- Arithmetic Progressions Chapter 6- Co-ordinate Geometry Chapter 7- Triangles Chapter 8- Circles Chapter 9- Constructions Chapter 10- Trigonometric Ratios Chapter 11- Trigonometric Identities Chapter 12- Heights and Distances Chapter 13- Areas Related to Circles Chapter 14- Surface Areas and Volumes Chapter 15- StatisticsRD SHARMA Solutions for CBSE Class 10 Subjects
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