Question

A letter is to be picked at random from the English alphabet. If each letter is equally likely to be selected, what is the probability of selecting a consonant? Consonants are letters except for a, e, i, o, and u. Write your answer in the simplest form of fraction.

Answer 1

The English alphabet consists of 26 letters in total. The vowels in the English alphabet are: a, e, i, o, and u. This gives us a total of 5 vowels.

To find the number of consonants, we subtract the number of vowels from the total number of letters:

\[
\text{Number of consonants} = \text{Total letters} - \text{Number of vowels} = 26 - 5 = 21
\]

Now, we want to determine the probability of selecting a consonant. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Thus, the probability \( P \) of selecting a consonant is given by:

\[
P(\text{consonant}) = \frac{\text{Number of consonants}}{\text{Total number of letters}} = \frac{21}{26}
\]

This fraction is already in its simplest form because 21 and 26 have no common factors other than 1.

Therefore, the probability of selecting a consonant is

\[
\boxed{\frac{21}{26}}.
\]