Statistics and probability

Question

Dr. Emmett Brown has a bag of M&Ms. He has 7 green M&Ms, 12 brown M&Ms, 3 blue M&Ms, and 5 red M&Ms.

What is the probability that Emmett selects a blue M&M and a green M&M without replacement?

Use 4 decimals***

Answer 1

There are 27 M and M total in the bag. There are 3 blue and 7 green M and M.

He can select a blue one then a green one:

The probability of selecting a blue one first is 3/27, which leaves us with 26 left.

The probability of then selecting a green one is 7/26

The probability of both occurring is 3/27 * 7/26 = 21/702

Or he can select a green one then a blue one

The probability of selecting a green one first is 7/27, which leaves us with 26 left.

The probability of then selecting a blue on is 3/26

The probability of both occurring is 7/27 * 3/26 = 21/702

The probability of selecting a blue and a green (in either order is):

21/702 + 21/702 = 42/702 = 0.0598