Question

You randomly choose a word from the first 100 words. what is the probability that the word starts with a vowel and has more than four letters?

Answer 1

22/100 starts with vowel
21/ 100 more than 4 letters

Answer 2

462/ 10000 is the probability of the word that starts with a vowel and has more than 4 letters?

Answer 3

@SmoothMath is this right?

Answer 4

I'm confused a little by this problem... the first 100 words of what? Of a specific book or something?

Answer 5

ok a book, i added the information right under the problem. we had to count how many words had 4 letters from the book and how many words started with a vowel from the first 100 words in the book

Answer 6

it said pick any book to do that.

Answer 7

and from that i got 22/100 words that started with a vowel and 21/100 words that had more than 4 letters

Answer 8

you have to count the number of words with both > 4 letters and start with a vowel
divide by 100 to get the probability

Answer 9

@SmoothMath do you know how to solve this?

Answer 10

@SmoothMath are you there?

Answer 11

since it is AND you have to multiply the probabilities together

Answer 12

so is my answer right?

Answer 13

462/10000

Answer 14

yes, assuming that your counts are correct as far as words with vowels and words with 4 letters.

Answer 15

ok thanks~!

Answer 16

of course though i would reduce that fraction

Answer 17

Actually, that's false. Let me show you why. Here's a sentence with 10 words in it:
I used an axe and chopped all of the lumber.

Supposing I pick a random word, what's the probability that it will begin with a vowel and also be longer than 4 letters? There are 7 words beginning with vowels, and there are 2 words longer than 4 letters, but there are 0 words that being with vowels AND have more than 4 letters, so obviously the probability is 0.

Answer 18

The trick here is that it's not really 2 events. It's one event. Instead of counting the number of words beginning with vowels and counting the number of words longer than 4 letters, you should be counting the number of words that satisfy both conditions.