Selecting/Choosing a Single/One Letter/Character from a word

Problem 1

A single letter is selected at random from the word RIGHTEOUSLY. The probability and odds that it is a consonant is
Ans :
7
11
, 7 : 4, 4 : 7

Solution

In the word RIGHTEOUSLY

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 = 11C1
=
11
1
= 11

Let

A : the event of the letter selected being a consonant

For Event A

In the word RIGHTEOUSLY

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 7C14C011C1

Number of Favorable Choices

= Number of ways in which one letter which is a consonant can be selected from the total 7 favorable letters

⇒ mA = 7C1
=
7
1
= 7

Probability of the letter selected being a consonant

⇒ Probability of occurrence of Event A

=
Number of Favorable Choices for the Event
Total Number of Possible Choices for the Experiment
⇒ P(A) =
mA
n
=
7
11

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc = n − mA
= 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

= mA : mAc

= 7 : 4

against

Odds against the letter selected being a consonant

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 4 : 7

Practice Problems

A single letter is selected at random from the word PROBABILITY. The probability and odds that it is a vowel is:
Author : The Edifier