A bag contains 6 blue marbles, 3 red marbles and 6 green marbles. You reach into the bag and select a marble and note its color. You place the marble back. You select a second marble and note its color and place it back. You pick a marble for the 3rd time and note its color. What are the chances of selecting three marbles NOT of the same color?

Step-by-step explanation:

So first we set this problem up

3 Red + 7 Blue + 5 Green = 15 Total Marbles

The chances of picking a different coloured marble each time is the product of the probabilities of picking an individual colour.

Since we have 15 total marbles, therfore number of possible outcomes of picking a red marble is 3/15=1/5

Similarly, number of possible outcomes of picking a blue marble is 7/15

number of possible outcomes of picking a green marble is 5/15=1/3

Therefore, the probabilities of picking a different colour each time=(1/5) (7/15) (1/3)=7/225