Question

Each of the letters in the word MATHEMATICS is represented by a letter tile in a bag. Stacey picks three letters, without replacement. To the nearest whole percent, which is the probability that she'll get all vowels?

a) 2%
b) 3%
c) 5%
d) 6%

Answer 1

count the vowels and total letters first... there are 4 vowels and 11 total letters.

so the chance of drawing a vowel on the first draw is 4/11.

Answer 2

but you need to multiply by the chances of drawing vowels on the next two draws also.

Answer 3

So.. what do I do? o,o

Answer 4

it says "without replacement". So after you draw the first letter, you only have 10 letters left. The chance of drawing one of the three remaining vowels out of the 10 remaining letters is 3/10. Same idea for the third draw... less vowels and letters remain, so it's s different fraction.

Answer 5

..I still don't get it, at all..

Answer 6

How did you get the 3/10?

Answer 7

11 letters, with 4 of them vowels: draw one, and the chance of a vowel is 4/11
Now there are only 10 letters left, and 3 vowels. chance of a vowel on 2nd draw is 3/10
On 3rd draw, there are only 9 letters left, and 2 vowels.. chance of drawing a vowel on the third try is 2/9.

Answer 8

You have to multiply these individual probabilities together though...

Like, for an easier example, if you were flipping a coin, the chance of heads the first flip is 50% or 1/2. The chance of flipping heads twice in a row is 1/2 * 1/2 = 1/4 or 25%.
The chance of three heads in a row is 1/2 * 1/2 * 1/2 = 1/8 = 12.5%