A bag contains a Blue a Red and a Yellow marble. If one marble is selected and then returned to the bag three times, what is the sample space of the repeated experiment?

Question

So, does that mean that I include all of them because it is returned?
Would it be like:
BBB, BBR, BBY, BYY, BYR, BYB, BRR, BRB, BRY, RRR, RRY, RRY, RYY, RBR, RBR, RBY, RBB, YYY, YYB, YYR, YBY, YBR, YBB, YRY, YRB, YRR

Answer 1

Yes, that is correct. Since the marble is returned to the bag after each selection, all possibilities should be included in the sample space. The sample space for the repeated experiment of selecting one marble and returning it to the bag three times would be:

BBB, BBR, BBY, BYY, BYR, BYB, BRR, BRB, BRY, RRR, RRY, RRY, RYY, RBR, RBR, RBY, RBB, YYY, YYB, YYR, YBY, YBR, YBB, YRY, YRB, YRR

There are a total of 27 possible outcomes in the sample space.

Answer 2

Does the order in which I make the combinations matter? Meaning, do I have to start by doing RRR, RRY, ......? Thank you.

Answer 3

In this case, the order of the combinations does not matter. The sample space consists of all possible combinations that can occur when selecting one marble and returning it to the bag three times. You do not have to follow a specific order when listing the combinations. The important thing is to include all possible outcomes. So, you can list the combinations in any order you prefer.