Question

A letter is chosen from English alphabet. Find the probability of the letter being:
a) A vowel
b) A letter comes after P
c) A vowel or a consonant
d) Not a vowel

Answer 1

We know,

$P\left(E\right)=\frac{\text{favorable outcome}}{\text{total outcomes}}$

Total letter in English alphabet = 26

(a) a vowel

Number of vowel = 5

$P\left(\text{getting a vowel}\right)=\frac{5}{26}$

(b) a letter comes after P

P is 16${}^{th}$ letter hence there will be 15 letters after P

$P\left(\text{getting a letter coming after P}\right)=\frac{15}{26}$

(c) a vowel or a consonant

Number of consonants = 21

Number of vowels = 5

$P\left(\text{getting a vowel or a consonant}\right)=\frac{5+21}{26}=1$

(d) not a vowel

Number of vowels = 5

$P\left(\text{getting a vowel}\right)=\frac{5}{26}$

$P\left(\text{getting not a vowel}\right)=1-P\left(\text{getting a vowel}\right)=1-\frac{5}{26}=\frac{21}{26}$