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 | = | 11C1 | ||
= |
| |||
= | 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 | 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 |
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
⇒ 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