Question

Suppose you select 2 letters at random from the word compute. Find each probability.

P(2 consonants)

Answer 1

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COMPUTE: There are 7 letters in the word.

1. P(2 vowels): Since O, U and E are vowels. There are 3 of them. So, the probability is 3/7, but because the 2nd time around cannot be repeated so 2/7. If you multiply them you get 6/49, which comes out 0.122448979591837 or rounded to 0.122. 12.2% is the probability that there will be two vowels when chosen at random.

3 * 2 = 6
7 7 49

2. P(2 consonants): Since C, M, P, T are consonants. There are 4 of them. So we do the same thing. The first probability is 4/7, but because one must be removed the second time around. The second time is 3/7. So you multiply them and get 12/49, which is 0.244897959183673 or 0.244. 24.4% is the probability that 2 constants will be chosen.

3. P(1 vowel, 1 consonant): Since O, U, E are vowels. The ratio is 3/7 for the first one. The second one is C, M, P, T. There are 4 of these, so 4/7. Once again multiply them and you get 12/49 or 24.4%.

Your answers:
P(2 V)-12.2%
P(2 C)-24.4% `
P(1V and 1C)-24.4%
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