There are 3 red marbles, 3 blue marbles, and 1 green marble in a bag. A marble is drawn at random from the bag and not replaced. Then a second marble is drawn. What are all the possible outcomes?

There are two mutually exclusive cases:

case 1: the first marble is green, then there are two outcomes for the second marble (red or blue).
case 2: the first marble is not green
then there are two possible outcomes for the first marble (R or B), and 3 possible outcomes for the second (R, G or B), making a total of 6 outcomes by the multiplication rule.
By the rule of addition, we add the outcomes of cases 1 and 2 to get
total outcomes = 2+6 = 8.

To determine all the possible outcomes, we need to consider the different combinations of marbles that can be drawn.

The first marble can be one of the 7 marbles in the bag - 3 red, 3 blue, and 1 green. Let's call the first marble drawn "Marble 1".

After drawing Marble 1, there are two scenarios for the second marble:

1. If Marble 1 is not replaced back into the bag:
- If Marble 1 is red, there are 6 marbles left in the bag - 2 red, 3 blue, and 1 green. The second marble ("Marble 2") can be any of these 6 marbles.
- If Marble 1 is blue, there are 6 marbles left in the bag - 3 red, 2 blue, and 1 green. The second marble ("Marble 2") can be any of these 6 marbles.
- If Marble 1 is green, there are 6 marbles left in the bag - 3 red, 3 blue, and 0 green. The second marble ("Marble 2") can be any of these 6 marbles.

2. If Marble 1 is replaced back into the bag after drawing:
- If Marble 1 is red, there are still 7 marbles in the bag - 3 red, 3 blue, and 1 green. The second marble ("Marble 2") can be any of these 7 marbles.
- If Marble 1 is blue, there are still 7 marbles in the bag - 3 red, 3 blue, and 1 green. The second marble ("Marble 2") can be any of these 7 marbles.
- If Marble 1 is green, there are still 7 marbles in the bag - 3 red, 3 blue, and 1 green. The second marble ("Marble 2") can be any of these 7 marbles.

By considering both scenarios, we can find all the possible outcomes:

1. Marble 1 is not replaced:
- If Marble 1 is red:
- Marble 2 can be red, blue, or green.
- If Marble 1 is blue:
- Marble 2 can be red, blue, or green.
- If Marble 1 is green:
- Marble 2 can be red, blue, or green.

2. Marble 1 is replaced:
- If Marble 1 is red:
- Marble 2 can be red, blue, green.
- If Marble 1 is blue:
- Marble 2 can be red, blue, green.
- If Marble 1 is green:
- Marble 2 can be red, blue, green.

Therefore, all the possible outcomes are: RR, RB, RG, BR, BB, BG, GR, GB.