Question

Two Balls are to be selected without replacement from a bag that contains one

red, one blue, one green and one orange ball. A) Use the counting principle to

determine the number of possible points in the sample space. Construct a tree

diagram and list the sample space.

Answer 1

The first experiment has $4$ possible outcomes since there are $4$ different balls.

The second experiment has only $4-1=3$ possible outcomes since this experiment is done without replacement.

Therefore, the number of possible outcomes will be

$$4\cdot3=12$$

$$S=\{RB, RG,RO, BR, BG, BO,$$

$$GR, GB, GO, OR, OB, OG\}$$