Odds in favor/favour of an event  Odds against an event 
Odds in favor/favour of an event  Odds against an event 
Odds in favor/favour of an event 
⇒ Odds in favor of an event  =  Number of favourable choices : Number of unfavorable choices 
=  m : m^{c}  

(Or)  =  Number of successes : Number of failures 
=  m : (n  m) 
Total number of possible choices  =  2 {HEAD, TAIL} 
⇒ n  =  2 

Let
Number of favorable/favourable Choices (Or) Number of Successes  =  1 {TAIL} 
⇒ m_{K}  =  1 

Number of unfavorable/unfavourable Choices (Failures)  
=  Total Number of possible choices  Number of Favorable/Favourable choices (successes)  
⇒ m_{K}^{c}  =  n  m_{K} 

=  2  1  
=  1 
Therefore,
Odds in favor/favour  =  Number of favorable/favourable choices : Number of unfavorable/unfavourable choices 
(Or)  =  Number of Successes : Number of Failures 
=  m_{K} : m_{K}^{c}  

=  1 : 1 
Total number of possible choices  =  6 {1, 2, 3, 4, 5, 6} 
⇒ n  =  6 

Let
Number of favorable/favourable Choices (Or) Number of Successes  =  2 {FIVE, SIX} 
⇒ m_{H}  =  2 

Number of unfavorable/unfavourable Choices (Failures)  
=  Total Number of possible choices  Number of Favorable/Favourable choices (successes)  
⇒ m_{H}^{c}  =  n  m_{H} 

=  6  2  
=  4 
Therefore,
Odds in favor/favour  =  Number of favorable/favourable choices : Number of unfavorable/unfavourable choices 
(Or)  =  Number of Successes : Number of Failures 
=  m_{H} : m_{H}^{c}  

=  2 : 4  
=  1 : 2 
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Odds against an event 
⇒ Odds against an event  =  Number of unfavourable choices : Number of favorable choices 
=  m^{c} : m  

(Or)  =  Number of failures : Number of successes 
=  (n  m) : m 
Total number of possible choices  =  2 {HEAD, TAIL} 
⇒ n  =  2 

Let
Number of favorable/favourable Choices (Or) Number of Successes  =  1 {TAIL} 
⇒ m_{G}  =  1 

Number of unfavorable/unfavourable Choices (Or) Number of Failures  =  Total No. of possible choices  No. of Favourable choices (Successes). 
⇒ m_{G}^{c}  =  n  m_{G} 

=  2  1  
=  1 
Therefore,
Odds against  =  No. of unfavourable choices : No. of favorable choices 
(Or)  =  No. of failures : No. of successes 
=  m_{G}^{c} : m_{G}  

=  1 : 1 
Total number of possible choices  =  6 {1, 2, 3, 4, 5, 6} 
⇒ n  =  6 

Let
Number of favorable/favourable Choices (Or) Number of Successes  =  5 {ONE, TWO, THREE, FOUR, FIVE} 
⇒ m_{T}  =  5 

Number of unfavorable/unfavourable Choices (Or) Number of Failures  =  Total No. of possible choices  No. of Favourable choices (Successes). 
⇒ m_{T}^{c}  =  n  m_{T} 

=  6  5  
=  1 
Therefore,
Odds against  =  No. of unfavourable choices : No. of favorable choices 
(Or)  =  No. of failures : No. of successes 
=  m_{T}^{c} : m_{T}  

=  1 : 5 
Expressing odds for and against 
Odds being a ratio can be expressed in all the different forms in which a mathematical ratio can be expressed.
The ratio a : b can be expressed as 

Total number of possible choices  =  6 {1, 2, 3, 4, 5, 6} 
⇒ n  =  6 

Let
Number of favorable/favourable Choices (Or) Number of Successes  =  4 {ONE, TWO, FOUR, FIVE} 
⇒ m_{F}  =  5 

Number of unfavorable/unfavourable Choices  =  Total No. of possible choices  No. of Favourable choices. 
(Or) Number of Failures  =  Total No. of possible choices  No. of Successes. 
⇒ m_{F}^{c}  =  n  m_{F} 

=  6  4  
=  2 
Therefore,
Odds in favor  =  No. of favourable choices : No. of unfavorable choices 
(Or)  =  No. of successes : No. of failures 
=  m_{F} : m_{F}^{c}  

=  4 : 2  
=  2 : 1 
Odds against  =  No. of unfavourable choices : No. of favorable choices 
(Or)  =  No. of failures : No. of successes 
=  m_{F}^{c} : m_{F}  

=  2 : 4  
=  1 : 2 
odds in favor  = 
 
= 
 
=  2  
odds against  = 
 
= 
 
= 

odds in favor  = 
 
= 
 
=  2.0  
odds against  = 
 
= 
 
= 
 
=  0.5 
... 789 ... 
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