Roulette is a very popular game in many American casinos. In roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2, ..., 35, 36. The number of the arc on which the ball stops is the outcome of one play of the game. The numbers are also colored in the following manner:

Red: 1,3,5,7,9,12,14,16,18,19,21.23,25,27,30,32.34,36 Black: 2.4,6,8,10,11,13,15,17,20,22,24.26,28,29,31,33,35 Greerz: 00,O Players may place bets on the table in a variety of ways, including bets on odd, even, red, black, high, low, etc. Define the following events:

A: (Outcome is an odd number (00 and 0 are considered neither odd nor even)]

B: (Outcome is a black number]

C: {Outcome is a low number (1-18))

a. Define the event AnB as a specific set of sample points.

b. Define the event AUB as a specific set of sample points.

C. Find P(A). P(B), P(AnB), P(AUB), and P(C)

by summing the probabilitics of the appropriate sample points.

d. Define the event AflBnC as a specific set of sample points.

e. Find P(AUB) using the additive rule. Are events A and B mutually exclusive? Why?

f. Find P(AnBnC) by summing the probabilities of thc sample points given in part d.

g. Define the event (AUBUC) as a specific set of sample points.

h. Find P(AUBUC) by summing the probabilities of the sample points given in part g.