Final answer:
The probability of any one vowel being generated in the computer game is 0.032 or 3.2%. This is calculated by first determining the total probability of all consonants (which is 0.84) and then subtracting from 1 to find the total vowel probability, which is then divided by 5 as there are 5 vowels.
Step-by-step explanation:
To find the probability of any one vowel being generated in the computer game, let us first understand the distribution of letters in the game based on the given probabilities. Each of the 21 consonants has a probability of p = 0.04 of being selected. Since there are only 26 letters in the alphabet and we already accounted for the 21 consonants, there are 5 vowels left (a, e, i, o, u).
The total probability of all events must sum to 1. Therefore, the probability of a vowel being generated is 1 minus the combined probability of all consonants. Given there are 21 consonants and each has a probability of 0.04, the total probability for consonants is 21 times 0.04, which equals 0.84. Subtracting this from 1: 1 - 0.84 = 0.16.
Since the vowels have an equal probability of being generated and there are 5 vowels, we divide the vowel probability by 5 to find the probability of any one vowel being selected. Hence, the probability of any one vowel being generated is 0.16 / 5 = 0.032 or 3.2%.