# If a letter is chosen at random from the English alphabet,

Question:

If a letter is chosen at random from the English alphabet, find the probability that the letter is chosen is

(i) a vowel

(ii) a consonant

Solution:

(i) We know that,

Probability of occurrence of an event

$=\frac{\text { Total no. of Desired outcomes }}{\text { Total no. of outcomes }}$

Total possible outcomes are alphabets from a to $z$

Desired outcomes are $a, e, i, o, u$

Total no. of outcomes are 26 and desired outputs are 5

Therefore, the probability of picking a vowel

$=\frac{5}{26}$

Conclusion: Probability of choosing a vowel is $\frac{5}{26}$

(ii) We know that,

Probability of occurrence of an event

$=\frac{\text { Total no. of Desired outcomes }}{\text { Total no.of outcomes }}$

Total possible outcomes are all alphabets from a to z

Desired outcomes are all alphabets except $a, e, i, o, u$

Total no.of outcomes are 26 and desired outputs are 21

Therefore, the probability of picking a consonant

$=\frac{21}{26}$

Conclusion: Probability of choosing a consonant is $\frac{21}{26}$