# 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 7C1 4C0 11C1

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