Question

Consider a five-letter word chosen randomly. What is the probability that the first two letters are vowels and the last three are consonants? Explain your answer.

Answer 1

The probability that the first two letters are vowels and the last three are consonants can be calculated using the formula for probability. The probability is approximately 0.0010.

Step-by-step explanation:

To find the probability, we need to determine how many five-letter words can be formed with two vowels followed by three consonants.

There are 4 vowels (a, e, i, o) and 21 consonants (excluding sometimes vowels y, w, u) in the English alphabet.

The probability can be calculated as:

P(first two letters are vowels and last three letters are consonants) = P(choose a vowel for the first letter) * P(choose a vowel for the second letter) * P(choose a consonant for the third letter) * P(choose a consonant for the fourth letter) * P(choose a consonant for the fifth letter)

= (4/26) * (4/25) * (21/24) * (20/23) * (19/22)

= 0.0010057 (rounded to 4 decimal places)