Question

A bag contains 10 red, 3 blue, and 2 yellow marbles. If 3 marbles are selected one at a time with replacement, find the probability that all three are different colors

Answer 1

4/225

Explanation:

To get 3 marbles that all three are different colors, we need to get a red, blue, and yellow marble (not necessarily in that order)

So we get the probability of getting each with replacement (meaning they are all out of 15) and multiply them.

The probability of getting a red is:

10/15 = 2/3

The probability of getting a blue is:

3/15 = 1/5

The probability of getting a yellow is:

2/15

So to get all 3 different colors:

2/3 * 1/5 * 2/15 = 4/225