Question

In a word game, you choose a tile from a bag, replace it, and then choose another. If there are 28 vowels and 12 consonants, what is the probability you will choose a consonant and then a vowel? WILL GIVE MEDAL

Answer 1

\[P(\text{consonant}) =\frac{\text{# of consonants}}{\text{total # of letters}}\]
\[ P(\text{vowel)}=\frac{\text{# of vowels}}{\text{total # of letters}}\]

\( P(\text{consonant then vowel})=P(\text{consonant})\times P(\text{vowel})\)

Notice that the total number of letters won't change when you're picking the vowel on the 2nd pick because you replaced the letter (it is back in the bag, so there are again the same number of letters as in the 1st pick)