Question

Determine the following probabilities. Enter your final answers as reduced fractions.

A single digit between
0
and
9
is randomly chosen, and a single letter from A to Z is randomly chosen.

Find the probability that the number is
6
and the letter is a consonant.

Answer 1

Explanation:

There are 10 possible outcomes for the digit (0-9) and 26 possible outcomes for the letter (A-Z). Since the choices are independent, the probability of selecting a 6 as the digit and a consonant as the letter is the product of the probabilities of each event occurring separately.

There are 21 consonants in the English alphabet, so the probability of selecting a consonant is 21/26. The probability of selecting a 6 is 1/10.

Therefore, the probability of selecting a 6 and a consonant is:

P(6 and consonant) = P(6) × P(consonant)

= 1/10 × 21/26

= 21/260

= 3/40

Hence, the probability that the number is 6 and the letter is a consonant is 3/40.