Answer:
[tex]P(Consonant\ then\ Vowel) = \frac{14}{55}[/tex]
Step-by-step explanation:
Given
Word: PROBABILITY
[tex]n(Word) = 11[/tex]
Required
Determine P(Consonant then Vowel)
Frist we need to list out the consonants;
Consonants = PRBBLTY
[tex]n(Consonants) = 7[/tex]
Then Vowels
Vowels = OAII
[tex]n(Vowels) = 4[/tex]
[tex]P(Consonant\ then\ Vowel) = P(Consonants)\ and\ P(Vowels)[/tex]
[tex]P(Consonant\ then\ Vowel) = \frac{n(Consonants)}{n(Words)} \ and\ \frac{n(Vowels)}{n(Words) - 1}[/tex]
We used n(words) - 1 for the vowels because it's probability without replacement. So, when the consonant is picked, the length of letters reduced by 1
So, we have:
[tex]P(Consonant\ then\ Vowel) = \frac{7}{11} \ and\ \frac{4}{11 - 1}[/tex]
[tex]P(Consonant\ then\ Vowel) = \frac{7}{11} \ *\ \frac{4}{10}[/tex]
[tex]P(Consonant\ then\ Vowel) = \frac{7}{11} \ *\ \frac{2}{5}[/tex]
[tex]P(Consonant\ then\ Vowel) = \frac{14}{55}[/tex]
