Question

You select a card at random. The cards are labeled with the word "Probability" as seen below. Without replacing each card, you choose a second card. P(consonant then vowel) =

Answer 1

`P(Consonant\ then\ Vowel) = (14)/(55)`

Explanation:

Given

Word: PROBABILITY

`n(Word) = 11`

Required

Determine P(Consonant then Vowel)

Frist we need to list out the consonants;

Consonants = PRBBLTY

`n(Consonants) = 7`

Then Vowels

Vowels = OAII

`n(Vowels) = 4`

`P(Consonant\ then\ Vowel) = P(Consonants)\ and\ P(Vowels)`

`P(Consonant\ then\ Vowel) = (n(Consonants))/(n(Words)) \ and\ (n(Vowels))/(n(Words) - 1)`

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:

`P(Consonant\ then\ Vowel) = (7)/(11) \ and\ (4)/(11 - 1)`

`P(Consonant\ then\ Vowel) = (7)/(11) \ *\ (4)/(10)`

`P(Consonant\ then\ Vowel) = (7)/(11) \ *\ (2)/(5)`

`P(Consonant\ then\ Vowel) = (14)/(55)`