# Suppose you select a letter from the word ALGEBRA. What's the probability of selecting two consonants? A vowel & consonant? Two vowels?

Nov 1, 2017

1) $p = \frac{2}{7}$

2) $p = \frac{2}{7}$

3) $p = \frac{1}{7}$

#### Explanation:

In the word ALGEBRA (7 letters) there are 4 consonants, then the probability of selecting first 1 consonant and then another 1 is the product of single probabilities, but, before the second selection, the number of letters is 6 and the number of consonants is 3, then:

1) $p = \frac{4}{7} \cdot \frac{3}{6} = \frac{2}{7}$

2) There are 3 vowels, then if I wish to select first a vowel and then a consonant,

$p = \frac{3}{7} \cdot \frac{4}{6} = \frac{2}{7}$

3) There are 3 vowels and 7 letters at the first selection, but 2 vowels and 6 letters at the second one, then

$p = \frac{3}{7} \cdot \frac{2}{6} = \frac{1}{7}$