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?

Answer 1

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.