Answer: 729/8000
Step-by-step explanation: To find the probability of selecting three red marbles from the bag, we need to consider the total number of marbles and the number of red marbles.
Given:
- 9 red marbles
- 4 blue marbles
- 7 yellow marbles
Since we are replacing each marble before selecting the next one, the total number of marbles remains the same throughout the selection process.
The probability of selecting a red marble on the first draw is:
9 red marbles / (9 red marbles + 4 blue marbles + 7 yellow marbles) = 9/20.
Since we are replacing the marble, the probability of selecting a red marble on the second draw is also 9/20.
Similarly, the probability of selecting a red marble on the third draw is also 9/20.
To find the probability of all three marbles being red, we multiply the individual probabilities together:
(9/20) * (9/20) * (9/20) = 729/8000.
So, the probability that all three marbles selected are red when each marble is replaced is 729/8000.