A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you dra

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green?

We are drawing without replacement. Take each draw probability:

1. First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25
2. Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24

Since both events are independent, we have:
P(Green) * P(Green) = 8/25 * 7/24
P(Green) * P(Green) = 56/600

Using our GCF Calculator, we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8.
P(Green) * P(Green) = 7/75