Question

You select a card at random from the cards that make up the word “replacement”. Without replacing the card, you choose a second card. Find the probability of choosing a vowel and then not a vowel. There is 1 letter for each card.

Answer 1

what is the probability you get a vowel on the first try?

Answer 2

1/4?

Answer 3

how many vowels?

Answer 4

it is a matter of counting
count the number of vowels, then count the total number of letters
it is the ratio of vowels to the total

Answer 5

so it would be 4/11?

Answer 6

yes

Answer 7

now one letter is gone, it is a vowel
how many not vowels are left, and how many letters are left?

Answer 8

we usually call those "consonants "

Answer 9

3/10, and 7/11?

Answer 10

hold on
one vowel is gone, because you know you picked a vowel first
that leaves 10 cards left, and 7 consonants right?

Answer 11

so the probability that the second card is a consonant if you know the first card is a vowel is \(\frac{7}{10}\)

Answer 12

you will find your answer by multiplying
\[\frac{4}{11}\times \frac{7}{10}\]

Answer 13

so it would be 14/55

Answer 14

yes