If two letters are taken at random from the word HOME, what is theProbability that none of the letters would be vowels?(a) 1/6(b) 1/2(c) 1/3(d) ¼
Question
If two letters are taken at random from the word HOME, what is theProbability that none of the letters would be vowels?(a) 1/6(b) 1/2(c) 1/3(d) ¼
Solution
The word HOME has 4 letters in total, 2 of which are vowels (O, E) and 2 are consonants (H, M).
We are looking for the probability that none of the letters selected are vowels, which means we are only interested in the consonants.
The number of ways to select 2 letters out of 2 (H, M) is 2C2 = 1.
The total number of ways to select 2 letters out of 4 (H, O, M, E) is 4C2 = 6.
So, the probability that none of the letters would be vowels is 1/6.
Therefore, the answer is (a) 1/6.
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