Question

Michael has a box of colored balls. It contains two red balls, three 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 five 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 S denote the sample space of the experiment, and let E denote the event that the ball drawn at the beginning is blue.
What is n(S)?

What is n(E′)?

Andre's dog Fifi knows fifteen tricks, five of which are interesting. Fifi does a show by performing either two or three different tricks one after another. If the first two tricks are both interesting, she will perform a third trick; otherwise, she only performs two tricks.
How many different shows could Fifi do?

Answer 1

Thank u.