Question

If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?

• A. $\frac{1}{6}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{11}{49}$

Answer 1

The correct option is A $\frac{1}{6}$

$P$(first letter is not vowel) $=\frac{2}{4}$

$P$(second letter is not vowel) $=\frac{1}{3}$

Therefore, probability that none of letters would be vowels is:$\frac{2}{4}\times \frac{1}{3}=\frac{2}{12}=\frac{1}{6}$