No. 
Problems & Solutions [Click Hide/Show to display the solutions below the question] 
01. 
A single letter is selected at random from the word “RIGHTEOUSLY”. The probability and odds that it is a consonant is:

Number of letters in the word "RIGHTEOUSLY" = 11 {R, I, G, H, T, E, O, U, S, L, Y}
In the experiment of selecting a letter from the letters of the word "RIGHTEOUSLY"
Total No. of Possible Choices 
= 
Number of ways in which a unique letter can be drawn from the total 11

⇒ n 
= 
^{11}C_{1} 

= 


= 
11 
Where there are repetitions, drawing either of the repeated letters would mean the same. Thus only the unique letters are considered for finding the number of possible choices.

Let "A" be the event of the letter selected being a vowel
For Event "A"
Number of consonants in the letters of the word "RIGHTEOUSLY" = 7 {R, G, H, T, S, L, Y}
Number of Favourable/Favorable Choices 
= 
The number of ways in which one letter which is a consonant can be selected from the total 7 consonants

⇒ m_{A} 
= 
^{7}C_{1} 

= 


= 
7 
Probability of the letter drawn being a vowel
⇒ Probability of occurrence of Event "A" 
= 
Number of Favourable/Favorable Choices for the Event  Total Number of Possible Choices for the Experiment 

⇒ P(A) 
= 


= 

• Odds
No. of UnFavorable Choices

= 
Total No. of possible choices − No. of Favorable choices 
⇒ m_{A}^{c} 
= 
n − m_{A}


= 
11 − 7 

= 
4 
» in favor/favour
Odds in Favour of the letter selected being a consonant
⇒ Odds in Favor/Favour of Event "A" 
= 
No. of Favourable Choices : No. of UnFavorable Choices 

= 
m_{A} : m_{A}^{c} 

= 
7 : 4 
» against
Odds against the letter selected being a consonant
⇒ Odds against Event "A" 
= 
No. of UnFavourable Choices : No. of Favorable Choices 

= 
m_{A}^{c} : m_{A} 

= 
4 : 7 

No. 
Problems & Solutions [Click Hide/Show to display the solutions below the question] 
01. 
A single letter is selected at random from the word “PROBABILITY”. The probability and odds that it is a vowel is:

Number of letters in the word "PROBABILITY" = 11 {P, R, O, B, A, B, I, L, I, T, Y}
Number of unique letters in the word "PROBABILITY" = 9 {P, R, O, B, A, I, L, T, Y}
In the experiment of selecting a letter from the letters of the word "PROBABILITY"
Total No. of Possible Choices 
= 
Number of ways in which a unique letter can be drawn from the total 9

⇒ n 
= 
^{9}C_{1} 

= 


= 
9 
Where there are repetitions, drawing either of the repeated letters would mean the same. Thus only the unique letters are considered for finding the number of possible choices.

Let "A" be the event of the letter selected being a vowel
For Event "A"
Number of vowels in the unique letters = 3 {O, A, I}
Number of Favourable/Favorable Choices 
= 
The number of ways in which one letter which is a vowel can be selected from the total 3 vowels

⇒ m_{A} 
= 
^{3}C_{1} 

= 


= 
3 
Probability of the letter drawn being a vowel
⇒ Probability of occurrence of Event "A" 
= 
Number of Favourable/Favorable Choices for the Event  Total Number of Possible Choices for the Experiment 

⇒ P(A) 
= 


= 


= 

• Odds
No. of UnFavorable Choices

= 
Total No. of possible choices − No. of Favorable choices 
⇒ m_{A}^{c} 
= 
n − m_{A}


= 
9 − 3 

= 
6 
» in favor/favour
Odds in Favour of the letter selected being a vowel
⇒ Odds in Favor/Favour of Event "A" 
= 
No. of Favourable Choices : No. of UnFavorable Choices 

= 
m_{A} : m_{A}^{c} 

= 
3 : 6 

= 
1 : 2 
» against
Odds against the letter selected being a vowel
⇒ Odds against Event "A" 
= 
No. of UnFavourable Choices : No. of Favorable Choices 

= 
m_{A}^{c} : m_{A} 

= 
6 : 3 

= 
2 : 1 

No. 
Problems for Practice 
01. 


