Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. A password of this type is chosen at random. What is the probability that the password does not have any vowels?
A) 0.20
B) 0.44
C) 0.65
D) 0.85

Question

Quizplus · Accepted Answer

There are 26 letters in the alphabet, and 5 of them are vowels (A, E, I, O, U). Therefore, there are 21 consonants. The probability of choosing a consonant for each of the two letters is (21/26). For the three digits, any digit from 0 to 9 can be chosen, so the probability for each digit is 1. The probability that the password does not have any vowels is (21/26) * (21/26) * 1 * 1 * 1 = 0.65.

Suppose a Password Must Consist of Two Letters Followed by Three