To calculate the probability of drawing a green marble for each of the four possible outcomes, we need to consider the number of ways that outcome can occur and divide it by the total number of possible outcomes.
Here are the four different ways the game could end:
1. The first marble drawn is green.
- There is only one green marble, and there are a total of four marbles. So the probability of this outcome is 1/4.
2. The second marble drawn is green.
- This outcome can occur if the first marble drawn is not green (3 red marbles out of 4 left) and the second marble is green (1 green marble out of 3 left). So the probability of this outcome is (3/4) * (1/3) = 1/4.
3. The third marble drawn is green.
- This outcome can occur if the first two marbles drawn are not green (3 red marbles out of 4 left after the first draw, and 2 red marbles out of 3 left after the second draw) and the third marble is green (1 green marble out of 2 left). So the probability of this outcome is (3/4) * (2/3) * (1/2) = 1/4.
4. The fourth (last) marble drawn is green.
- This outcome can only occur if the first three marbles drawn are not green (3 red marbles out of 4 left after the first draw, 2 red marbles out of 3 left after the second draw, and 1 red marble out of 2 left after the third draw) and the fourth marble is green (1 green marble out of 1 left). So the probability of this outcome is (3/4) * (2/3) * (1/2) * (1/1) = 1/4.
Therefore, the probability of drawing a green marble for each of the four possible outcomes is 1/4 for each outcome.