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Page 1
Probability
Practice Set 5.1
Q. 1. How many possibilities are there in each of the following?
(1) Vanita knows the following sites in Maharashtra. She is planning to visit one
of them in her summer vacation.
Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli,
Raigad, Matheran, Anandavan.
(2) Any day of a week is to be selected randomly.
(3) Select one card from the pack of 52 cards.
(4) One number from 10 to 20 is written on each card. Select one card randomly.
Answer : (1) 8
Count the number of sites.
(2) 7
In a week comprising of 7 days, there are 7 ways to select any day .
(3) 52
From a deck of 52 cards, we can select any one card in 52 ways.
(4) 11
There are 11 total ways of selecting a card randomly .
Practice Set 5.2
Q. 1. For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating a
digits.
Answer :
(1) Sample Space, S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
Page 2
Probability
Practice Set 5.1
Q. 1. How many possibilities are there in each of the following?
(1) Vanita knows the following sites in Maharashtra. She is planning to visit one
of them in her summer vacation.
Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli,
Raigad, Matheran, Anandavan.
(2) Any day of a week is to be selected randomly.
(3) Select one card from the pack of 52 cards.
(4) One number from 10 to 20 is written on each card. Select one card randomly.
Answer : (1) 8
Count the number of sites.
(2) 7
In a week comprising of 7 days, there are 7 ways to select any day .
(3) 52
From a deck of 52 cards, we can select any one card in 52 ways.
(4) 11
There are 11 total ways of selecting a card randomly .
Practice Set 5.2
Q. 1. For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating a
digits.
Answer :
(1) Sample Space, S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
Number of events in Sample Space S, n(S) = 12
(2) Sample Space, S = {23, 25, 32, 35, 52, 53}
Number of events in Sample Space S, n(S) = 6
Q. 2. The arrow is rotated and it stops randomly on the disc. Find out on which
colour it may stop.
Answer : Sample Space, S = {Red, Purple, Orange, Yellow, Blue, Green}
Number of events in Sample Space S, n(S) = 6
Q. 3. In the month of March 2019, find the days on which the date is a multiple of
5. (see the given page of the calendar)
Answer : The days on which the date is a multiple of 5 are as follows:
Multiples of 5 are 5, 10, 15, 20, 25, 30
So,
a) Tuesday (5 March 2019)
b) Sunday (10 March 2019)
c) Friday (15 March 2019)
d) Wednesday (20 March 2019)
e) Monday (25 March 2019)
Page 3
Probability
Practice Set 5.1
Q. 1. How many possibilities are there in each of the following?
(1) Vanita knows the following sites in Maharashtra. She is planning to visit one
of them in her summer vacation.
Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli,
Raigad, Matheran, Anandavan.
(2) Any day of a week is to be selected randomly.
(3) Select one card from the pack of 52 cards.
(4) One number from 10 to 20 is written on each card. Select one card randomly.
Answer : (1) 8
Count the number of sites.
(2) 7
In a week comprising of 7 days, there are 7 ways to select any day .
(3) 52
From a deck of 52 cards, we can select any one card in 52 ways.
(4) 11
There are 11 total ways of selecting a card randomly .
Practice Set 5.2
Q. 1. For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating a
digits.
Answer :
(1) Sample Space, S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
Number of events in Sample Space S, n(S) = 12
(2) Sample Space, S = {23, 25, 32, 35, 52, 53}
Number of events in Sample Space S, n(S) = 6
Q. 2. The arrow is rotated and it stops randomly on the disc. Find out on which
colour it may stop.
Answer : Sample Space, S = {Red, Purple, Orange, Yellow, Blue, Green}
Number of events in Sample Space S, n(S) = 6
Q. 3. In the month of March 2019, find the days on which the date is a multiple of
5. (see the given page of the calendar)
Answer : The days on which the date is a multiple of 5 are as follows:
Multiples of 5 are 5, 10, 15, 20, 25, 30
So,
a) Tuesday (5 March 2019)
b) Sunday (10 March 2019)
c) Friday (15 March 2019)
d) Wednesday (20 March 2019)
e) Monday (25 March 2019)
f) Saturday(30 March 2019)
Q. 4. Form a ‘Road safety commitee’ of two, from 2 boys (B1, B2) and 2 girls(G1,
G2). Complete the following activity to write the sample space.
Answer : a) Committee of 2 boys = B 1, B2
b) Committee of 2 girls= G 1, G2
c) Committee of one boy and one girl=Any of the event given in sample space given
below is possible
Sample Space, S={B 1G1, B1G2, B2G1, B2G2}
Practice Set 5.3
Q. 1 A. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.
Answer :
Sample space, S = {1, 2, 3, 4, 5, 6}
Number of sample points, n(S) = 6
A = {2, 4, 6} , n(A) = 3
B = {1, 3, 5} , n(B) = 3
C = {2, 3, 5} , n(C) = 3
Page 4
Probability
Practice Set 5.1
Q. 1. How many possibilities are there in each of the following?
(1) Vanita knows the following sites in Maharashtra. She is planning to visit one
of them in her summer vacation.
Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli,
Raigad, Matheran, Anandavan.
(2) Any day of a week is to be selected randomly.
(3) Select one card from the pack of 52 cards.
(4) One number from 10 to 20 is written on each card. Select one card randomly.
Answer : (1) 8
Count the number of sites.
(2) 7
In a week comprising of 7 days, there are 7 ways to select any day .
(3) 52
From a deck of 52 cards, we can select any one card in 52 ways.
(4) 11
There are 11 total ways of selecting a card randomly .
Practice Set 5.2
Q. 1. For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating a
digits.
Answer :
(1) Sample Space, S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
Number of events in Sample Space S, n(S) = 12
(2) Sample Space, S = {23, 25, 32, 35, 52, 53}
Number of events in Sample Space S, n(S) = 6
Q. 2. The arrow is rotated and it stops randomly on the disc. Find out on which
colour it may stop.
Answer : Sample Space, S = {Red, Purple, Orange, Yellow, Blue, Green}
Number of events in Sample Space S, n(S) = 6
Q. 3. In the month of March 2019, find the days on which the date is a multiple of
5. (see the given page of the calendar)
Answer : The days on which the date is a multiple of 5 are as follows:
Multiples of 5 are 5, 10, 15, 20, 25, 30
So,
a) Tuesday (5 March 2019)
b) Sunday (10 March 2019)
c) Friday (15 March 2019)
d) Wednesday (20 March 2019)
e) Monday (25 March 2019)
f) Saturday(30 March 2019)
Q. 4. Form a ‘Road safety commitee’ of two, from 2 boys (B1, B2) and 2 girls(G1,
G2). Complete the following activity to write the sample space.
Answer : a) Committee of 2 boys = B 1, B2
b) Committee of 2 girls= G 1, G2
c) Committee of one boy and one girl=Any of the event given in sample space given
below is possible
Sample Space, S={B 1G1, B1G2, B2G1, B2G2}
Practice Set 5.3
Q. 1 A. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.
Answer :
Sample space, S = {1, 2, 3, 4, 5, 6}
Number of sample points, n(S) = 6
A = {2, 4, 6} , n(A) = 3
B = {1, 3, 5} , n(B) = 3
C = {2, 3, 5} , n(C) = 3
Q. 1 B. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
Two dice are rolled simultaneously,
Event A : The sum of the digits on upper faces is a multiple of 6.
Event B : The sum of the digits on the upper faces is minimum 10.
Event C : The same digit on both the upper faces.
Answer : Sample space, 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)}
Number of sample points, n(S) = 36
A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}, n(A) = 6
B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)} , n(B) = 6
C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)} , n(C) = 6
Q. 1 C. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
Three coins are tossed simultaneously.
Condition for event A : To get at least two heads.
Condition for event B : To get no head.
Condition for event C : To get head on the second coin.
Answer : Sample Space, S = {HHH, HHT, HTT, HTH, THT, TTH, THH, TTT}
Number of sample points, n(S) = 8
To get at least two heads ,A = {HHH, HHT, HTH, THH}
n(A) = 4
To get no head, B = {TTT}
n(B) = 1
To get head on the second coin ,C = {HHH, HHT, THH}
n(C) = 3
Page 5
Probability
Practice Set 5.1
Q. 1. How many possibilities are there in each of the following?
(1) Vanita knows the following sites in Maharashtra. She is planning to visit one
of them in her summer vacation.
Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli,
Raigad, Matheran, Anandavan.
(2) Any day of a week is to be selected randomly.
(3) Select one card from the pack of 52 cards.
(4) One number from 10 to 20 is written on each card. Select one card randomly.
Answer : (1) 8
Count the number of sites.
(2) 7
In a week comprising of 7 days, there are 7 ways to select any day .
(3) 52
From a deck of 52 cards, we can select any one card in 52 ways.
(4) 11
There are 11 total ways of selecting a card randomly .
Practice Set 5.2
Q. 1. For each of the following experiments write sample space ‘S’ and number of
sample points n(S).
(1) One coin and one die are thrown simultaneously.
(2) Two digit numbers are formed using digits 2, 3 and 5 without repeating a
digits.
Answer :
(1) Sample Space, S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}
Number of events in Sample Space S, n(S) = 12
(2) Sample Space, S = {23, 25, 32, 35, 52, 53}
Number of events in Sample Space S, n(S) = 6
Q. 2. The arrow is rotated and it stops randomly on the disc. Find out on which
colour it may stop.
Answer : Sample Space, S = {Red, Purple, Orange, Yellow, Blue, Green}
Number of events in Sample Space S, n(S) = 6
Q. 3. In the month of March 2019, find the days on which the date is a multiple of
5. (see the given page of the calendar)
Answer : The days on which the date is a multiple of 5 are as follows:
Multiples of 5 are 5, 10, 15, 20, 25, 30
So,
a) Tuesday (5 March 2019)
b) Sunday (10 March 2019)
c) Friday (15 March 2019)
d) Wednesday (20 March 2019)
e) Monday (25 March 2019)
f) Saturday(30 March 2019)
Q. 4. Form a ‘Road safety commitee’ of two, from 2 boys (B1, B2) and 2 girls(G1,
G2). Complete the following activity to write the sample space.
Answer : a) Committee of 2 boys = B 1, B2
b) Committee of 2 girls= G 1, G2
c) Committee of one boy and one girl=Any of the event given in sample space given
below is possible
Sample Space, S={B 1G1, B1G2, B2G1, B2G2}
Practice Set 5.3
Q. 1 A. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.
Answer :
Sample space, S = {1, 2, 3, 4, 5, 6}
Number of sample points, n(S) = 6
A = {2, 4, 6} , n(A) = 3
B = {1, 3, 5} , n(B) = 3
C = {2, 3, 5} , n(C) = 3
Q. 1 B. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
Two dice are rolled simultaneously,
Event A : The sum of the digits on upper faces is a multiple of 6.
Event B : The sum of the digits on the upper faces is minimum 10.
Event C : The same digit on both the upper faces.
Answer : Sample space, 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)}
Number of sample points, n(S) = 36
A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}, n(A) = 6
B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)} , n(B) = 6
C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)} , n(C) = 6
Q. 1 C. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
Three coins are tossed simultaneously.
Condition for event A : To get at least two heads.
Condition for event B : To get no head.
Condition for event C : To get head on the second coin.
Answer : Sample Space, S = {HHH, HHT, HTT, HTH, THT, TTH, THH, TTT}
Number of sample points, n(S) = 8
To get at least two heads ,A = {HHH, HHT, HTH, THH}
n(A) = 4
To get no head, B = {TTT}
n(B) = 1
To get head on the second coin ,C = {HHH, HHT, THH}
n(C) = 3
Q. 1 D. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the
digits.
Condition for event A : The number formed is even
Condition for event B : The number formed is divisible by 3.
Condition for event C : The number formed is greater than 50.
Answer : Sample Space, S= {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35,
40, 41, 42, 43,45, 50, 51, 52, 53, 54}
Number of sample points, n(S) = 25
The number formed is even , A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}
n(A) = 13
The number formed is divisible by 3, B = {12, 15, 21, 24, 30, 42, 45, 51, 54}
n(B) = 9
The number formed is greater than 50,C = {51, 52, 53, 54} n(C) = 4
Q. 1 E. Write sample space ‘S’ and number of sample point n(S) for each of the
following experiments. Also write events A, B, C in the set form and write n(A),
n(B), n(C).
From three men and two women, environment committee of two persons is to be
formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed
Condition for event C : There should not be a woman member.
Answer : Sample Space, S = {M1M2, M1M3, M1F1, M1F2, M2M3, M2F1, M2F2, M3F1, M3F2,
F1F2}
Number of sample points, n(S) = 10
There must be at least one woman member , A = {M1F1, M1F2, M2F1, M2F2, M3F1, M3F2,
F1F2}
n(A) = 7
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FAQs on Textbook Solutions: Probability - Mathematics Class 10 (Maharashtra SSC Board)
| 1. What is the basic definition of probability in mathematics? |  |
Ans. Probability is a branch of mathematics that deals with the likelihood or chance of different outcomes occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. The probability of an event can be calculated using the formula: Probability = (Number of favorable outcomes) / (Total number of outcomes).
| 2. How do you calculate the probability of a single event? | |
Ans. To calculate the probability of a single event, you need to determine the number of favorable outcomes for that event and divide it by the total number of possible outcomes. For example, if you roll a die, the probability of rolling a 3 is 1 (favorable outcome) divided by 6 (total outcomes), which equals 1/6.
| 3. What is the difference between theoretical and experimental probability? | |
Ans. Theoretical probability is based on the expected outcomes in a perfect scenario, calculated using mathematical reasoning. For example, the theoretical probability of flipping a coin and getting heads is 1/2. Experimental probability, on the other hand, is based on actual experiments and observations. It is calculated by conducting trials and recording the outcomes, which may differ from the theoretical probability due to various factors.
| 4. Can you explain what a sample space is in probability? | |
Ans. A sample space in probability is the set of all possible outcomes of a random experiment. For example, if you toss a coin, the sample space is {Heads, Tails}. If you roll a die, the sample space is {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities accurately.
| 5. What are independent and dependent events in probability? | |
Ans. Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other. For example, flipping a coin and rolling a die are independent events. Dependent events, however, are events where the occurrence of one event affects the occurrence of another. For instance, drawing two cards from a deck without replacement is a dependent event because the outcome of the first draw influences the second.
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Sep 23, 2025
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