Selecting/Choosing a Single/One Letter/Character from a word
Problem 1
7 
11 
Solution
Number of letters
= 11
{R, I, G, H, T, E, O, U, S, L, Y}
Experiment :
Selecting a letter from the letters of the word RIGHTEOUSLY
Total Number of Possible Choices
= Number of ways in which one letter can be drawn from the total 11
⇒ n  =  ^{11}C_{1}  
= 
 
=  11 
Let
A : the event of the letter selected being a consonant
For Event A
Number of consonants
= 7
{R, G, H, T, S, L, Y}
Favorable (consonants)  Unfavorable (Others)  Total  

Available  7  4  11 
To Choose  1  0  1 
Choices  ^{7}C_{1}  ^{4}C_{0}  ^{11}C_{1} 
Number of Favorable Choices
= Number of ways in which one letter which is a consonant can be selected from the total 7 favorable letters
⇒ m_{A}  =  ^{7}C_{1}  
= 
 
=  7 
Probability of the letter selected being a consonant
⇒ Probability of occurrence of Event A
= 

⇒ P(A)  = 
 
= 

Odds
Number of Unfavorable Choices= Total Number of possible choices − Number of Favorable choices
⇒ m_{A}^{c}  =  n − m_{A} 
=  11 − 7  
=  4 
in favor
Odds in Favor of the letter selected being a consonant⇒ Odds in Favor of Event A
= Number of Favorable Choices : Number of Unfavorable Choices
= m_{A} : m_{Ac}
= 7 : 4
against
Odds against the letter selected being a consonant⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= m_{Ac} : m_{A}
= 4 : 7