Question

Andrew has $2.00 in quarters in his pocket, including three state quarters. He takes two quarters out of his pocket. What is the probability that they are not state quarters?
A 3/8
B 5/8
C 3/14
D 5/14
Show work please!

Answer 1

$2.00 in quarters is 8 quarters, since 1 quarter is 25 cents.
Out of those 8 quarters, only 3 are state quarters.
That means 5 are not state quarters.
So there is a 5/8 chance that the first quarter he takes out is not a state quarter.
If it is not, then there are 3 state quarters and 7 total quarters left, which means a 4/7 chance that the second quarter is not a state quarter.
To find the probability of both of these quarters not being state quarters, multiply the probabilities by each other.
4/7 • 5/8 = 20/56
Now simplify:
20/56 = 10/28 = 5/14
5/14 is in simplest form, so it is the answer.
So the answer is D. 5/14.