Michael has a box of colored balls. It contains four red balls, two green balls,

Question

Michael has a box of colored balls. It contains four red balls, two green balls, one purple ball, two yellow balls, and five blue balls. Michael will perform an experiment which goes as follows. First, a ball is drawn from the box at random, the color of the ball is noted (R for red, G for green, etc.), and the ball is set aside (i.e. not replaced into the box). The next stage of the experiment depends on the color of the ball Michael draws. If the ball is red, he will draw another ball and note its color. If the ball he draws at the beginning is green, he will draw six more balls, simultaneously and at random, and note how many of the balls he has drawn are red. Otherwise (if the ball drawn at the beginning is neither green nor red), he will flip a coin and note the result (H for heads, T for tails. Thus, for example, BH, RR, and G2 are three possible outcomes of the experiment.

Let SS denote the sample space of the experiment, and let EE denote the event that the ball drawn at the beginning is blue.
What is n(S)n(S)?   
What is n(E?)n(E?)?

Explanation / Answer

The sample space for this experiment is:

{ RR, RG, RY, RP, RB, G1, G2, G3, G4, BH, BT, YH, YT, PH, PT }

So the number of possible outcomes for this experiment are:

n(S) = 15

When the ball drawn at the beginning is blue, then there are only two possible outcomes: { BH, BT }

So, number of possible outcomes for the event B are:

n(E) = 2

Assuming that E' denotes that the event E does not occur:

So, n(E') = n(s) - n(E) = 15-2 = 13

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