In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 21 vowels and 15 consonants, what is the probability you will choose a consonant and then a vowel?
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Let's do one drawing at a time.
When you start, there are how many total tiles?
Yes. There are a total of 36 tiles.
15 of the tiles are consonants.
21 tiles are vowels.
The probability of an outcome of an event happening is the number of ways the desired outcome can happen divided by the total number of outcomes.
Let's look at the first drawing.
You want a consonant.
There are 15 consonants out of 36 tiles.
P(consonant) = 15/36
For the second drawing, the tile that was drawn before is replaced. That means the second drawing is independent of the first drawing. You have again 36 total tiles. Now you want to draw a vowel. There are 21 vowels, so the probability of drawing a vowel in the second drawing is
P(vowel) = 21/36
The probability of two independent events happening is the product of their probabilities.
P(consonant then vowel) = P(consonant) * P(vowel)
P(consonant then vowel) = 15/36 * 21/36 =5/12 * 7/12 = 35/144