Textbook: Probability | Mathematics Class 10 (Maharashtra SSC Board) PDF Download

 Page 1


113
5
Probability
Let’s discuss.
Teacher : Friends, this box contains folded chits. The number of chits is exactly the 
same as the number of students in our class. Each student should pick one 
chit. Names of different plants are written on the chits. No two chits bear 
the same name of the plant. Let us see who gets the chit having the name 
'Basil'. Make a line in the order of your roll numbers. No one will unfold the 
chit until the last student takes his chit. 
Aruna : Sir, I am the first one in a line, but I do not want to pick a chit first, as the 
possibility of getting 'basil' chit from all the chits is very low. 
Zarina  :   Sir, I am the last student in the row, I do not want to pick the chit at last as 
the chit containing the name 'basil' will most likely be picked up by some 
one else before my turn. 
The first and the last student feel that for each of them, the possibility of 
getting the chit having the name 'basil' is very low. The above conversation 
indicates the thinking of less or more possibility. 
 We use the following words to express the possibility in our daily conversation. 
 · Probable   · may be    · impossible 
 · sure    · nearly   · 50 - 50
 Read the following statements regarding predictions (possibilities for the future). 
 ·  Most probably the rain will start from today. 
 ·  The inflation is likely to rise. 
 ·  It is impossible to defeat Indian cricket team in the next match. 
 ·  I will surely get first class. 
 · There is no possibility of Polio infection if a child is given the polio vaccine in time. 
· Probability : Introduction  ·  Random experiment and its outcome
·  Sample space and event ·  Probability of an event
Let’s study.
Page 2


113
5
Probability
Let’s discuss.
Teacher : Friends, this box contains folded chits. The number of chits is exactly the 
same as the number of students in our class. Each student should pick one 
chit. Names of different plants are written on the chits. No two chits bear 
the same name of the plant. Let us see who gets the chit having the name 
'Basil'. Make a line in the order of your roll numbers. No one will unfold the 
chit until the last student takes his chit. 
Aruna : Sir, I am the first one in a line, but I do not want to pick a chit first, as the 
possibility of getting 'basil' chit from all the chits is very low. 
Zarina  :   Sir, I am the last student in the row, I do not want to pick the chit at last as 
the chit containing the name 'basil' will most likely be picked up by some 
one else before my turn. 
The first and the last student feel that for each of them, the possibility of 
getting the chit having the name 'basil' is very low. The above conversation 
indicates the thinking of less or more possibility. 
 We use the following words to express the possibility in our daily conversation. 
 · Probable   · may be    · impossible 
 · sure    · nearly   · 50 - 50
 Read the following statements regarding predictions (possibilities for the future). 
 ·  Most probably the rain will start from today. 
 ·  The inflation is likely to rise. 
 ·  It is impossible to defeat Indian cricket team in the next match. 
 ·  I will surely get first class. 
 · There is no possibility of Polio infection if a child is given the polio vaccine in time. 
· Probability : Introduction  ·  Random experiment and its outcome
·  Sample space and event ·  Probability of an event
Let’s study.
114
 The adjoining picture shows a ‘toss’ before a cricket match. 
 What are the possibilities ?
   or  
 
 
 So here there are    possibilities. 
 
Activity 1 : Let each student in the class toss a coin once. What will you get?
     (Teacher writes the observations on the board in a table.) 
Possibilities
 (H ) ( T)
Number of students 
. . . . . . 
Activity 2 :  Ask each student to toss the same coin twice. What are the possibilities?
Possibilities
H H HT TH TT
Number of students 
Activity 3 :  Now throw a die, once. What are the different  possibilities of getting dots on 
  the upper face ?
                     
   Each of these is a possible result of throwing a die.
Let’s learn.
   Random Experiment
 The experiment in which all possible results are known in advance but none of 
them can be predicted with certainty and there is equal possibility for each result is 
known as a ‘Random experiment’. 
 For example, Tossing a coin, throwing a die, picking a card from a set of cards 
bearing numbers from 1 to 50, picking a card from a pack of well shuffled playing 
cards, etc. 
·
·
·
· · ·
· · ·
·   ·
·   ·
·    ·
·    ·
·
   ·
      ·
·
Page 3


113
5
Probability
Let’s discuss.
Teacher : Friends, this box contains folded chits. The number of chits is exactly the 
same as the number of students in our class. Each student should pick one 
chit. Names of different plants are written on the chits. No two chits bear 
the same name of the plant. Let us see who gets the chit having the name 
'Basil'. Make a line in the order of your roll numbers. No one will unfold the 
chit until the last student takes his chit. 
Aruna : Sir, I am the first one in a line, but I do not want to pick a chit first, as the 
possibility of getting 'basil' chit from all the chits is very low. 
Zarina  :   Sir, I am the last student in the row, I do not want to pick the chit at last as 
the chit containing the name 'basil' will most likely be picked up by some 
one else before my turn. 
The first and the last student feel that for each of them, the possibility of 
getting the chit having the name 'basil' is very low. The above conversation 
indicates the thinking of less or more possibility. 
 We use the following words to express the possibility in our daily conversation. 
 · Probable   · may be    · impossible 
 · sure    · nearly   · 50 - 50
 Read the following statements regarding predictions (possibilities for the future). 
 ·  Most probably the rain will start from today. 
 ·  The inflation is likely to rise. 
 ·  It is impossible to defeat Indian cricket team in the next match. 
 ·  I will surely get first class. 
 · There is no possibility of Polio infection if a child is given the polio vaccine in time. 
· Probability : Introduction  ·  Random experiment and its outcome
·  Sample space and event ·  Probability of an event
Let’s study.
114
 The adjoining picture shows a ‘toss’ before a cricket match. 
 What are the possibilities ?
   or  
 
 
 So here there are    possibilities. 
 
Activity 1 : Let each student in the class toss a coin once. What will you get?
     (Teacher writes the observations on the board in a table.) 
Possibilities
 (H ) ( T)
Number of students 
. . . . . . 
Activity 2 :  Ask each student to toss the same coin twice. What are the possibilities?
Possibilities
H H HT TH TT
Number of students 
Activity 3 :  Now throw a die, once. What are the different  possibilities of getting dots on 
  the upper face ?
                     
   Each of these is a possible result of throwing a die.
Let’s learn.
   Random Experiment
 The experiment in which all possible results are known in advance but none of 
them can be predicted with certainty and there is equal possibility for each result is 
known as a ‘Random experiment’. 
 For example, Tossing a coin, throwing a die, picking a card from a set of cards 
bearing numbers from 1 to 50, picking a card from a pack of well shuffled playing 
cards, etc. 
·
·
·
· · ·
· · ·
·   ·
·   ·
·    ·
·    ·
·
   ·
      ·
·
115
Ace of 
heart
Ace of 
spade
Ace of 
club
Ace of 
diamond
      Outcome
 Result of a random experiment is known as an ‘Outcome’. 
 Ex. (1) In a random experiment of tossing a coin - there are only two outcomes. 
   Head (H) or Tail (T)   
 (2)  In a random experiment of throwing a die, there are 6 outcomes, 
according to the number of dots on the six faces of the die. 
     1  or  2  or  3  or   4  or   5  or  6.
    (3) In a random experiment of picking a card bearing numbers from 1 to 50,  
there are 50 outcomes. 
    (4) A card is drawn randomly from a pack of well shuffled playing cards. 
There are 52 cards in a pack as shown below. 
Total cards 52
    
        26 red cards         26 black cards   
 
 13 heart cards 13 diamond cards  13 club cards    13 spade cards 
                
 In a pack of playing cards there are 4 sets, 
namely heart, diamond, club and spade. In each 
set there are 13 cards as King, Queen, Jack, 10, 9, 
8, 7, 6, 5, 4, 3, 2 and Ace. 
 King, Queen and Jack are known as face 
cards. In each pack of cards there are 4 cards of 
king, 4 cards of Queen and 4 cards of Jack. Thus 
total face cards are 12. 
 
       Equally Likely Outcomes
 If a die is thrown, any of the numbers from 1, 2, 3, 4, 5, 6 may appear on the 
upper face. It means that each number is equally likely to occur. However, if a die is 
so formed that a particular face come up most often, then that die is biased. In this case 
the outcomes are not likely to occur equally.
 Here, we assume that objects used for random experiments are fair or unbiased. 
 A given number of outcomes are said to be equally likely if none of them occurs 
A
A
A
A
Page 4


113
5
Probability
Let’s discuss.
Teacher : Friends, this box contains folded chits. The number of chits is exactly the 
same as the number of students in our class. Each student should pick one 
chit. Names of different plants are written on the chits. No two chits bear 
the same name of the plant. Let us see who gets the chit having the name 
'Basil'. Make a line in the order of your roll numbers. No one will unfold the 
chit until the last student takes his chit. 
Aruna : Sir, I am the first one in a line, but I do not want to pick a chit first, as the 
possibility of getting 'basil' chit from all the chits is very low. 
Zarina  :   Sir, I am the last student in the row, I do not want to pick the chit at last as 
the chit containing the name 'basil' will most likely be picked up by some 
one else before my turn. 
The first and the last student feel that for each of them, the possibility of 
getting the chit having the name 'basil' is very low. The above conversation 
indicates the thinking of less or more possibility. 
 We use the following words to express the possibility in our daily conversation. 
 · Probable   · may be    · impossible 
 · sure    · nearly   · 50 - 50
 Read the following statements regarding predictions (possibilities for the future). 
 ·  Most probably the rain will start from today. 
 ·  The inflation is likely to rise. 
 ·  It is impossible to defeat Indian cricket team in the next match. 
 ·  I will surely get first class. 
 · There is no possibility of Polio infection if a child is given the polio vaccine in time. 
· Probability : Introduction  ·  Random experiment and its outcome
·  Sample space and event ·  Probability of an event
Let’s study.
114
 The adjoining picture shows a ‘toss’ before a cricket match. 
 What are the possibilities ?
   or  
 
 
 So here there are    possibilities. 
 
Activity 1 : Let each student in the class toss a coin once. What will you get?
     (Teacher writes the observations on the board in a table.) 
Possibilities
 (H ) ( T)
Number of students 
. . . . . . 
Activity 2 :  Ask each student to toss the same coin twice. What are the possibilities?
Possibilities
H H HT TH TT
Number of students 
Activity 3 :  Now throw a die, once. What are the different  possibilities of getting dots on 
  the upper face ?
                     
   Each of these is a possible result of throwing a die.
Let’s learn.
   Random Experiment
 The experiment in which all possible results are known in advance but none of 
them can be predicted with certainty and there is equal possibility for each result is 
known as a ‘Random experiment’. 
 For example, Tossing a coin, throwing a die, picking a card from a set of cards 
bearing numbers from 1 to 50, picking a card from a pack of well shuffled playing 
cards, etc. 
·
·
·
· · ·
· · ·
·   ·
·   ·
·    ·
·    ·
·
   ·
      ·
·
115
Ace of 
heart
Ace of 
spade
Ace of 
club
Ace of 
diamond
      Outcome
 Result of a random experiment is known as an ‘Outcome’. 
 Ex. (1) In a random experiment of tossing a coin - there are only two outcomes. 
   Head (H) or Tail (T)   
 (2)  In a random experiment of throwing a die, there are 6 outcomes, 
according to the number of dots on the six faces of the die. 
     1  or  2  or  3  or   4  or   5  or  6.
    (3) In a random experiment of picking a card bearing numbers from 1 to 50,  
there are 50 outcomes. 
    (4) A card is drawn randomly from a pack of well shuffled playing cards. 
There are 52 cards in a pack as shown below. 
Total cards 52
    
        26 red cards         26 black cards   
 
 13 heart cards 13 diamond cards  13 club cards    13 spade cards 
                
 In a pack of playing cards there are 4 sets, 
namely heart, diamond, club and spade. In each 
set there are 13 cards as King, Queen, Jack, 10, 9, 
8, 7, 6, 5, 4, 3, 2 and Ace. 
 King, Queen and Jack are known as face 
cards. In each pack of cards there are 4 cards of 
king, 4 cards of Queen and 4 cards of Jack. Thus 
total face cards are 12. 
 
       Equally Likely Outcomes
 If a die is thrown, any of the numbers from 1, 2, 3, 4, 5, 6 may appear on the 
upper face. It means that each number is equally likely to occur. However, if a die is 
so formed that a particular face come up most often, then that die is biased. In this case 
the outcomes are not likely to occur equally.
 Here, we assume that objects used for random experiments are fair or unbiased. 
 A given number of outcomes are said to be equally likely if none of them occurs 
A
A
A
A
116
Practice Set 5.1
in preferance to others. For example if a coin is tossed, possibilities of getting head 
or tail are equal.  A die, having numbers from 1 to 6 on its different faces, is thrown. 
Check the possibility of getting one of the numbers. Here all the outcomes are eqully 
likely. 
Let’s think.
In which of the following experiments possibility of expected outcome is more?
 (1)  Getting 1 on the upper face when a die is thrown. 
 (2)  Getting head by tossing a coin. 
Let’s learn.
 Sample Space
 The set of all possible outcomes of a random experiment is called the sample 
space. It is denoted by ‘S’ or ‘?’ (A greek letter 'Omega'). Each element of sample 
space is called a ‘sample point’.  The number of elements in the set ‘S’ is denoted by  
n(S). If n(S) is finite, then the sample space is said to be a finite sample space. 
 Following are some examples of finite sample spaces. 
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. 
Page 5


113
5
Probability
Let’s discuss.
Teacher : Friends, this box contains folded chits. The number of chits is exactly the 
same as the number of students in our class. Each student should pick one 
chit. Names of different plants are written on the chits. No two chits bear 
the same name of the plant. Let us see who gets the chit having the name 
'Basil'. Make a line in the order of your roll numbers. No one will unfold the 
chit until the last student takes his chit. 
Aruna : Sir, I am the first one in a line, but I do not want to pick a chit first, as the 
possibility of getting 'basil' chit from all the chits is very low. 
Zarina  :   Sir, I am the last student in the row, I do not want to pick the chit at last as 
the chit containing the name 'basil' will most likely be picked up by some 
one else before my turn. 
The first and the last student feel that for each of them, the possibility of 
getting the chit having the name 'basil' is very low. The above conversation 
indicates the thinking of less or more possibility. 
 We use the following words to express the possibility in our daily conversation. 
 · Probable   · may be    · impossible 
 · sure    · nearly   · 50 - 50
 Read the following statements regarding predictions (possibilities for the future). 
 ·  Most probably the rain will start from today. 
 ·  The inflation is likely to rise. 
 ·  It is impossible to defeat Indian cricket team in the next match. 
 ·  I will surely get first class. 
 · There is no possibility of Polio infection if a child is given the polio vaccine in time. 
· Probability : Introduction  ·  Random experiment and its outcome
·  Sample space and event ·  Probability of an event
Let’s study.
114
 The adjoining picture shows a ‘toss’ before a cricket match. 
 What are the possibilities ?
   or  
 
 
 So here there are    possibilities. 
 
Activity 1 : Let each student in the class toss a coin once. What will you get?
     (Teacher writes the observations on the board in a table.) 
Possibilities
 (H ) ( T)
Number of students 
. . . . . . 
Activity 2 :  Ask each student to toss the same coin twice. What are the possibilities?
Possibilities
H H HT TH TT
Number of students 
Activity 3 :  Now throw a die, once. What are the different  possibilities of getting dots on 
  the upper face ?
                     
   Each of these is a possible result of throwing a die.
Let’s learn.
   Random Experiment
 The experiment in which all possible results are known in advance but none of 
them can be predicted with certainty and there is equal possibility for each result is 
known as a ‘Random experiment’. 
 For example, Tossing a coin, throwing a die, picking a card from a set of cards 
bearing numbers from 1 to 50, picking a card from a pack of well shuffled playing 
cards, etc. 
·
·
·
· · ·
· · ·
·   ·
·   ·
·    ·
·    ·
·
   ·
      ·
·
115
Ace of 
heart
Ace of 
spade
Ace of 
club
Ace of 
diamond
      Outcome
 Result of a random experiment is known as an ‘Outcome’. 
 Ex. (1) In a random experiment of tossing a coin - there are only two outcomes. 
   Head (H) or Tail (T)   
 (2)  In a random experiment of throwing a die, there are 6 outcomes, 
according to the number of dots on the six faces of the die. 
     1  or  2  or  3  or   4  or   5  or  6.
    (3) In a random experiment of picking a card bearing numbers from 1 to 50,  
there are 50 outcomes. 
    (4) A card is drawn randomly from a pack of well shuffled playing cards. 
There are 52 cards in a pack as shown below. 
Total cards 52
    
        26 red cards         26 black cards   
 
 13 heart cards 13 diamond cards  13 club cards    13 spade cards 
                
 In a pack of playing cards there are 4 sets, 
namely heart, diamond, club and spade. In each 
set there are 13 cards as King, Queen, Jack, 10, 9, 
8, 7, 6, 5, 4, 3, 2 and Ace. 
 King, Queen and Jack are known as face 
cards. In each pack of cards there are 4 cards of 
king, 4 cards of Queen and 4 cards of Jack. Thus 
total face cards are 12. 
 
       Equally Likely Outcomes
 If a die is thrown, any of the numbers from 1, 2, 3, 4, 5, 6 may appear on the 
upper face. It means that each number is equally likely to occur. However, if a die is 
so formed that a particular face come up most often, then that die is biased. In this case 
the outcomes are not likely to occur equally.
 Here, we assume that objects used for random experiments are fair or unbiased. 
 A given number of outcomes are said to be equally likely if none of them occurs 
A
A
A
A
116
Practice Set 5.1
in preferance to others. For example if a coin is tossed, possibilities of getting head 
or tail are equal.  A die, having numbers from 1 to 6 on its different faces, is thrown. 
Check the possibility of getting one of the numbers. Here all the outcomes are eqully 
likely. 
Let’s think.
In which of the following experiments possibility of expected outcome is more?
 (1)  Getting 1 on the upper face when a die is thrown. 
 (2)  Getting head by tossing a coin. 
Let’s learn.
 Sample Space
 The set of all possible outcomes of a random experiment is called the sample 
space. It is denoted by ‘S’ or ‘?’ (A greek letter 'Omega'). Each element of sample 
space is called a ‘sample point’.  The number of elements in the set ‘S’ is denoted by  
n(S). If n(S) is finite, then the sample space is said to be a finite sample space. 
 Following are some examples of finite sample spaces. 
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. 
117
S. 
No.
Random 
experiment
Sample space
Number 
of sample 
points in S
1
One coin is tossed S = {H, T)
n(S) = 2
2
Two coins are 
tossed
S = { HH, HT, TH, TT}
n(S) = 
3
Three coins are 
tossed
S = {HHH, HHT, HTH, THH, HTT, THT, 
TTH, TTT}
n(S) =  8
4
A die is thrown S = {1, 2, 3, 4, 5, 6}
n(S) = 
5
Two dice are 
thrown
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
6
A card is drawn 
from a pack 
bearing numbers 
from 1 to 25
S = {1, 2, 3, 4, .. .. ... .. .. .. .. .. .. .. .., 25} 
n(S) = 
7
A card is drawn 
from a well shuffled
pack of 52 playing 
cards. 
Diamond : Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, 
Queen, King
Spade : Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, 
Queen, King
Heart : Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, 
Queen, King
Club : Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, 
Queen, King
n(S) = 52
Let’s remember!
(i) The sample space for a coin tossed twice is the same as that of two coins tossed 
 simultaneously. The same is true for three coins. 
(ii) The sample space for a die rolled twice is the same as two dice rolled 
 simultaneously. 
Practice Set 5.2
(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