Probability - Chapter Notes, Class 9 Mathematics Class 9 Notes | EduRev

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Class 9 : Probability - Chapter Notes, Class 9 Mathematics Class 9 Notes | EduRev

 Page 1


 
 
PROBABILITY
The word Probability is commonly used to represent 
uncertainty of an event. 
 
Example 
(i) Probably, it may rain today. 
(ii) Probably, he may stand first in the class. 
 
So, Probability is used to mention the chances or possibilities 
of a thing to occur. In other words, it represents the 
chances/possibilities for an event to occur out of an 
operation/experiment. 
 
Example 
If we throw a dice, then we may obtain any number out of the 
six numbers of dice. In this case, throwing the dice is the 
experiment/operation and getting a particular number is an 
event. 
To study the ‘Probability’ mathematically, we will first study 
some terms related to ‘Probability’. 
 
1. Experiment 
The word ‘experiment’ means, the operation which produces 
the result. 
 
The experiments are divided into two categories. 
 
(i) Deterministic Experiment 
 Deterministic experiments are those experiments, which 
on repeating under same conditions produce same result. 
 
 Example 
 Science or engineering events under same conditions 
produce same or almost same results. 
 
(ii)  Probabilistic / Random Experiments 
 Probabilistic or random experiments are those 
experiments, which on repeating under same conditions 
do not produce same results. In other words, these 
experiments produce one single result out of several 
possible results. 
 
 Example 
Throwing a dice under same conditions will produce 
different results each time or maximum times.  
 
2. Event 
The result of an experiment is called event. These are 
following types of events: - 
 
(i) Elementary Event 
The basic result of a random experiment is called 
elementary event. That means, the final single result 
obtain by an experiment is called elementary events. 
 
Example 
(i) On tossing a can randomly, we either get head or tail. 
Then, 
H = Getting H (head) 
T = Getting T (tail) 
 
So, H and T are elementary events, which are the results 
of random experiment tossing the coin. 
  
(ii) On tossing two coins simultaneous, we get different 
combinations of head and tail. 
Then, 
HT = Getting head (H) on first and tail (T) on second. 
HH = Getting head (H) on first and head (H) on second 
TH = Getting tail (T) and first and head (H) on second 
TT = Getting tail (T) on first and tail (T) on second 
 
So, HT, HH, TH and TT are elementary events. 
 
(iii) On throwing a dice, we get different numbers 
Then, 
-
1
N Getting Number 1 
-
2
N Getting number 2 
-
3
N Getting number 3 
-
4
N Getting number 4 
-
5
N Getting number 5 
-
6
N Getting number 6 
 
So 
5 4 3 2 1
N , N , N , N , N and 
6
N are elementary events. 
  
(ii) Compound Event 
The result of a random experiment made up of more than one 
elementary event is called compound event.  
 
Example 
On throwing a dice, getting a number is elementary event. In 
such case, getting an event number is a compound event, 
which is made of three elementary events, i.e. getting number 
1, getting number 3 and getting number 5. 
 
(iii) Possible Event 
All the possible results, which may produced by the experiment 
are called possible events 
 
Example 
(i) On tossing a coin, we may get 2 possible results. 
H – Getting Head (H) 
T – Getting tail (T) 
 
So, number of possible events is 2, i.e. H and T. 
 
(ii) On throwing a dice, we may get 6 possible results. 
-
1
N Getting number 1 
-
2
N Getting number 2 
-
3
N Getting number 3 
-
4
N Getting number 4 
-
5
N Getting number 5 
-
6
N Getting number 6. 
So, number of possible events is 6, i.e. 
1
N ,
2
N ,
3
N ,
4
N ,
5
N ,
6
N 
 
Page 2


 
 
PROBABILITY
The word Probability is commonly used to represent 
uncertainty of an event. 
 
Example 
(i) Probably, it may rain today. 
(ii) Probably, he may stand first in the class. 
 
So, Probability is used to mention the chances or possibilities 
of a thing to occur. In other words, it represents the 
chances/possibilities for an event to occur out of an 
operation/experiment. 
 
Example 
If we throw a dice, then we may obtain any number out of the 
six numbers of dice. In this case, throwing the dice is the 
experiment/operation and getting a particular number is an 
event. 
To study the ‘Probability’ mathematically, we will first study 
some terms related to ‘Probability’. 
 
1. Experiment 
The word ‘experiment’ means, the operation which produces 
the result. 
 
The experiments are divided into two categories. 
 
(i) Deterministic Experiment 
 Deterministic experiments are those experiments, which 
on repeating under same conditions produce same result. 
 
 Example 
 Science or engineering events under same conditions 
produce same or almost same results. 
 
(ii)  Probabilistic / Random Experiments 
 Probabilistic or random experiments are those 
experiments, which on repeating under same conditions 
do not produce same results. In other words, these 
experiments produce one single result out of several 
possible results. 
 
 Example 
Throwing a dice under same conditions will produce 
different results each time or maximum times.  
 
2. Event 
The result of an experiment is called event. These are 
following types of events: - 
 
(i) Elementary Event 
The basic result of a random experiment is called 
elementary event. That means, the final single result 
obtain by an experiment is called elementary events. 
 
Example 
(i) On tossing a can randomly, we either get head or tail. 
Then, 
H = Getting H (head) 
T = Getting T (tail) 
 
So, H and T are elementary events, which are the results 
of random experiment tossing the coin. 
  
(ii) On tossing two coins simultaneous, we get different 
combinations of head and tail. 
Then, 
HT = Getting head (H) on first and tail (T) on second. 
HH = Getting head (H) on first and head (H) on second 
TH = Getting tail (T) and first and head (H) on second 
TT = Getting tail (T) on first and tail (T) on second 
 
So, HT, HH, TH and TT are elementary events. 
 
(iii) On throwing a dice, we get different numbers 
Then, 
-
1
N Getting Number 1 
-
2
N Getting number 2 
-
3
N Getting number 3 
-
4
N Getting number 4 
-
5
N Getting number 5 
-
6
N Getting number 6 
 
So 
5 4 3 2 1
N , N , N , N , N and 
6
N are elementary events. 
  
(ii) Compound Event 
The result of a random experiment made up of more than one 
elementary event is called compound event.  
 
Example 
On throwing a dice, getting a number is elementary event. In 
such case, getting an event number is a compound event, 
which is made of three elementary events, i.e. getting number 
1, getting number 3 and getting number 5. 
 
(iii) Possible Event 
All the possible results, which may produced by the experiment 
are called possible events 
 
Example 
(i) On tossing a coin, we may get 2 possible results. 
H – Getting Head (H) 
T – Getting tail (T) 
 
So, number of possible events is 2, i.e. H and T. 
 
(ii) On throwing a dice, we may get 6 possible results. 
-
1
N Getting number 1 
-
2
N Getting number 2 
-
3
N Getting number 3 
-
4
N Getting number 4 
-
5
N Getting number 5 
-
6
N Getting number 6. 
So, number of possible events is 6, i.e. 
1
N ,
2
N ,
3
N ,
4
N ,
5
N ,
6
N 
 
 
(iv) Favourable Events 
All the results, which may satisfy the given condition are called 
favourable events. 
 
Example 
(i) On tossing a coin and getting the tail, we have one 
favourable event. 
T = Getting tail 
 
(ii) On throwing a dice and getting a number greater than or 
equal to 5, we have two favourable events. 
-
5
N Getting number 5 
-
6
N Getting number 6 
 
3. Negation Of Event 
If E is an event, then negation of event E is NotE. In other 
words, the unfavourable results are called negation of event E. 
Negation of event is represented by a bar on the event. So, if 
event is E, then negation of event is E . 
 
Example 
On throwing a dice to get number 4. 
Event – Getting number 4, i.e. 
4
N 
So, 
Negation Of Event – Getting a number other than 4, i.e. 
2 1
N , N , 
5 3
N , N and 
6
N 
 
Probability 
Now, we will study Probability mathematically. That means, 
we will represent Probability in terms of numeric values. 
 
Let all the possible events = n 
Let all the favourable events = m 
Probability = P(A) 
Then, 
n
m
) A ( P = 
 
So, if there are n possible events of a random experiment, out 
of which there are m favourable events, then probability is the 
ratio of possible events and favourable events. 
 
1. If all possible events satisfy the condition, then the 
event is sure to happen. 
So, possible events = n 
Favourable events = m 
Then, probability 
P(A) = 
n
m
 
? 
n
n
) A ( P =       [Possible Events = Favourable Event] 
? 1 ) A ( P = 
 
? Probability of an event sure to happen = 1 
 
2. If no possible event satisfy the condition, then the 
event is sure not to happen. 
So, possible events = n 
Favourable event = m = 0 
Then, probability 
n
m
) A ( P = 
? 
n
0
) A ( P =          [m = 0] 
? 0 ) A ( P = 
 
? Probability of an event sure not to happen =0 
 
3. If there are n possible events and m favourable 
events, then there are  m n - unfavourable events. 
So, possible events = n 
Favourable events = m 
Unfavourable events = n – m 
Then, probability 
n
m
) A ( P =        ………………… (i) 
Also, probability of negation of event  
m
m n
) A ( P
-
=        ………………… (ii) 
So, 
n
m n
n
m
) A ( P ) A ( P
-
+ = + 
? 
n
m n m
) A ( P ) A ( P
- +
= + 
? 
n
n
) A ( P ) A ( P = + 
? 1 ) A ( P ) A ( P = + 
That means, 
) A ( P 1 ) A ( P - =     Or 
) A ( P 1 ) A ( P - = 
 
Example 
A card is drawn from a well-shuffled deck of playing cards. 
Find the probability of drawing: - 
(i) A face card. 
(ii) A red face card. 
 
We have, 
Total number of possible events ) n ( = Total Cards = 52 
 
(i) Ace, king, queen and jack are called face cards. 
There are 4 aces, 4 kings, 4 queens, 4 jacks in a pack of cards. 
Then, 
Number of fvourable events (m) = Total Face Cards 
  = 4 + 4 + 4 
  = 12 
So, Probability of getting a face card  
n
m
) A ( P = 
   = 
12
52
 
   = 
3
13
 
 
(ii) There are 2 red aces, 2 red kings, 2 red queens and 2 red 
jacks in a pack of cards. 
Then, 
Number of favourable events (m) =Total Number Of Red Faces  
  = 2 + 2 + 2 + 2 
  =8 
So, probability of getting a red face card 
n
m
) A ( P =   
   = 
52
8
 
   = 
13
2
 
 
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