02 - Let's Recap - Probability - Class 10 - Maths Class 10 Notes | EduRev

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Class 10 : 02 - Let's Recap - Probability - Class 10 - Maths Class 10 Notes | EduRev

 Page 1


 
 
(Probability is the extent to which something is likely to happen) 
 
1. Experimental (or) Empirical Probability:  
A probability that is based on the outcome of an actual experiment 
and adequate recording of the happening of an event. 
 
[say, E = event and P = Probability, then P(E) = Probability of an event E] 
 
 ( ) 
                                            
                      
 
  
2. Theoretical (or) Classical Probability:  
A probability that is based on the assumption about the occurrence of 
an event (E) rather than the outcome of an actual experiment. 
 
 ( ) 
                              
                        
 
 
3. Equally Likely Outcomes:  
Outcomes of an event are said to be ‘equally likely ’ when they have 
the same chance of occurring. It happens in case of an unbiased and a fair 
event.  
Example:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
 
 
Page 2


 
 
(Probability is the extent to which something is likely to happen) 
 
1. Experimental (or) Empirical Probability:  
A probability that is based on the outcome of an actual experiment 
and adequate recording of the happening of an event. 
 
[say, E = event and P = Probability, then P(E) = Probability of an event E] 
 
 ( ) 
                                            
                      
 
  
2. Theoretical (or) Classical Probability:  
A probability that is based on the assumption about the occurrence of 
an event (E) rather than the outcome of an actual experiment. 
 
 ( ) 
                              
                        
 
 
3. Equally Likely Outcomes:  
Outcomes of an event are said to be ‘equally likely ’ when they have 
the same chance of occurring. It happens in case of an unbiased and a fair 
event.  
Example:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
 
 
 
 
  
4. ELEMENTARY EVENT:  
An event having only a single outcome at a time.   
Example:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Either a Head (H) or a tail (T). (Equally likely to occur) 
 
5. SUM OF PROBABILITIES RULE:  
The sum of probabilities of all the elementary events of an experiment 
is one.   
 
Example 1:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
  P (1) + P (2) + P (3) + P (4) + P (5) + P (6) = 1 
 
Example 2:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Head (H) and tail (T). (Equally likely to occur) 
  P (H) + P (T) = 1 
 
 
 
Page 3


 
 
(Probability is the extent to which something is likely to happen) 
 
1. Experimental (or) Empirical Probability:  
A probability that is based on the outcome of an actual experiment 
and adequate recording of the happening of an event. 
 
[say, E = event and P = Probability, then P(E) = Probability of an event E] 
 
 ( ) 
                                            
                      
 
  
2. Theoretical (or) Classical Probability:  
A probability that is based on the assumption about the occurrence of 
an event (E) rather than the outcome of an actual experiment. 
 
 ( ) 
                              
                        
 
 
3. Equally Likely Outcomes:  
Outcomes of an event are said to be ‘equally likely ’ when they have 
the same chance of occurring. It happens in case of an unbiased and a fair 
event.  
Example:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
 
 
 
 
  
4. ELEMENTARY EVENT:  
An event having only a single outcome at a time.   
Example:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Either a Head (H) or a tail (T). (Equally likely to occur) 
 
5. SUM OF PROBABILITIES RULE:  
The sum of probabilities of all the elementary events of an experiment 
is one.   
 
Example 1:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
  P (1) + P (2) + P (3) + P (4) + P (5) + P (6) = 1 
 
Example 2:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Head (H) and tail (T). (Equally likely to occur) 
  P (H) + P (T) = 1 
 
 
 
 
 
 
 
6. COMPLEMENTARY EVENT:  
Complementary events are those events where the probability of one 
event excludes the happening of the other event. 
In general, it is true that for an event E, there also exists the 
complement of the event E ( E or not E). We also say that E and E are 
complementary events. 
 
  P ( E ) = 1   P (E)          P ( E )   P (E) = 1  
Example:  
Event (E) – getting a head (H) after tossing a coin. 
Complement event ( E ) – not getting a head (H) or getting a tail (T) 
 
7. IMPOSSIBLE EVENT:  
An event that has no chance of occurring. Probability of such an event 
that is impossible to occur is zero.  
 
  P (impossible event) = 0 
  
Example:  
Event- getting a seven in a single throw of a die. 
  P (getting a 7) = 
 
 
   
Note: There are only six possible outcomes in a single throw of a die (1, 2, 
3, 4, 5 and 6). Since no face of the die is marked 7, so there is no outcome 
favorable to 7. In other words, getting a 7 in a single throw of a die, is 
impossible. 
Page 4


 
 
(Probability is the extent to which something is likely to happen) 
 
1. Experimental (or) Empirical Probability:  
A probability that is based on the outcome of an actual experiment 
and adequate recording of the happening of an event. 
 
[say, E = event and P = Probability, then P(E) = Probability of an event E] 
 
 ( ) 
                                            
                      
 
  
2. Theoretical (or) Classical Probability:  
A probability that is based on the assumption about the occurrence of 
an event (E) rather than the outcome of an actual experiment. 
 
 ( ) 
                              
                        
 
 
3. Equally Likely Outcomes:  
Outcomes of an event are said to be ‘equally likely ’ when they have 
the same chance of occurring. It happens in case of an unbiased and a fair 
event.  
Example:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
 
 
 
 
  
4. ELEMENTARY EVENT:  
An event having only a single outcome at a time.   
Example:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Either a Head (H) or a tail (T). (Equally likely to occur) 
 
5. SUM OF PROBABILITIES RULE:  
The sum of probabilities of all the elementary events of an experiment 
is one.   
 
Example 1:  
Event- Throwing a die (An unbiased and a fair event) 
Outcomes- 1, 2, 3, 4, 5 and 6. (All are equally likely to occur) 
  P (1) + P (2) + P (3) + P (4) + P (5) + P (6) = 1 
 
Example 2:  
Event- Tossing a coin (An unbiased and a fair event) 
Outcomes- Head (H) and tail (T). (Equally likely to occur) 
  P (H) + P (T) = 1 
 
 
 
 
 
 
 
6. COMPLEMENTARY EVENT:  
Complementary events are those events where the probability of one 
event excludes the happening of the other event. 
In general, it is true that for an event E, there also exists the 
complement of the event E ( E or not E). We also say that E and E are 
complementary events. 
 
  P ( E ) = 1   P (E)          P ( E )   P (E) = 1  
Example:  
Event (E) – getting a head (H) after tossing a coin. 
Complement event ( E ) – not getting a head (H) or getting a tail (T) 
 
7. IMPOSSIBLE EVENT:  
An event that has no chance of occurring. Probability of such an event 
that is impossible to occur is zero.  
 
  P (impossible event) = 0 
  
Example:  
Event- getting a seven in a single throw of a die. 
  P (getting a 7) = 
 
 
   
Note: There are only six possible outcomes in a single throw of a die (1, 2, 
3, 4, 5 and 6). Since no face of the die is marked 7, so there is no outcome 
favorable to 7. In other words, getting a 7 in a single throw of a die, is 
impossible. 
 
 
 
 
8. SURE EVENT:  
An event that has 100% probability of occurring. Probability of such 
an event that is sure/certain to occur is one.  
 
 
  P (sure event) = 1 
  
Example:  
Event- getting a number less than seven in a single throw of a die. 
  P (getting a number less than 7) = 
 
 
   
Note: Since every face of a die is marked with a number less than 7 (1, 2, 3, 
4, 5 and 6), it is sure that we will always get a number less than 7 when it is 
thrown once. So the number of favourable outcomes is same as the number 
of all possible outcomes, which is 6. 
 
 
9. The probability of an event E is a number P(E) such that 
 
 
   ( )   
 
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