Question

In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 8 vowels and 12 consonants, what is the probability you will choose a consonant first and then a vowel?

Answer 1

Answer: 6/25

Explanation:

Number of vowels = 8

Number of consonants = 12

Total number of tiles in bag = (number of vowels + number of consonants)

Total = (12 + 8) = 20

Probability = (required outcomes / total possible outcome)

Probability of choosing a consonants = (number of consonants / total number of word tiles)

P( consonants) = 12 / 20 = 3/5

Since it is with replacement, total number of word tiles will still be 20

Probability of choosing a vowel = (number of vowels / total number of word tiles)

P( vowels) = 8 / 20 = 2/5

Therefore,

P(constant then vowel) = 3/5 * 2/5 = 6/25