To find the sample space of the experiment where one marble is selected and returned to the bag three times, we consider the combinations of the three marble colors: Blue (B), Red (R), and Yellow (Y).
Since each draw is independent and we are selecting a marble three times, each selection can result in one of the three colors. Therefore, the sample space consists of all possible ordered triples of these colors for three draws.
The possible combinations of selections can be represented as three positions (one for each draw) filled with B, R, and Y.
The total possible combinations are calculated as: \[ 3 \times 3 \times 3 = 27 \]
The combinations are:
- BBB, RRR, YYY (all the same color)
- RRB, RRY, RYB, RYY, BRB, BRY, BYB, BYY (two of one color and one of another)
- RBB, YRR, YRY, YRB, YBR, YBB (various combinations)
- RYB, BBR, BYR, BYY, ... and so on.
After reviewing the given options, the correct sample space that includes all 27 possible outcomes is:
4) RRR, RRY, RRB, RYR, RYB, RYY, RBR, RBY, RBB, BBB, BBY, BBR, BYB, BYR, BYY, BRB, BRY, BRR, YYY, YYB, YYR, YBY, YBR, YBB, YRY, YRB, YRR
Thus, the correct answer is option 4.