# Probability: 3 colors of balls in a bag

A basket contains 4 black, 2 blue, and 5 green balls. A sample of 3 balls is drawn. Find the probabilities that the sample, drawn without replacement, contains the following

All blue balls

Exactly 2 black balls

2 green balls and 1 blue ball

© BrainMass Inc. brainmass.com October 10, 2019, 12:08 am ad1c9bdddfhttps://brainmass.com/math/probability/probability-colors-balls-bag-280073

#### Solution Preview

I am going to answer them in a different order, for purposes of explanation.

All blue balls : Student, this case is easy: zero! Since there are only 2 blue balls, we can never get all blues in a sample of three!

2 green balls and 1 blue ball : Letting G be a green ball and B be a blue ball, we can do this three ways: BGG, GBG, or GGB. Let's look at each case:

B on first draw: 2/11 (2 of the 11 in the basket ...

#### Solution Summary

Details on each case and how the probability is calculated.

$2.19