Set Theory

Part I: Set Theory

Look up a roulette wheel diagram..The following sets are defined:

A = the set of red numbers
B = the set of black numbers
C = the set of green numbers
D = the set of even numbers
E = the set of odd numbers
F = {1,2,3,4,5,6,7,8,9,10,11,12}

From these, determine each of the following
AUB
A∩D
B∩C
CUE
B∩F
E∩F

Part II: Graphs and Trees
Create a tree that models the following scenario. A player decided to play a maximum of 4 times, betting on read each time. The player will quit after losing twice. In the tree, any possible last plays will be an ending point of the tree. Branches of the tree should indicate the winning or losing, and how that affects whether a new play is made.

Part IV: Combinatories and Probability
In the roulette game, what is the probability of an outcome of:

·          Any odd number

·          Any green number

·          Any number that is red or green

·          Any number that is red and even

You are asked by a state government official to investigate whether under a proposed license plate system, there will be enough license plate codes for the state. There are 2 schemes proposed:

·         Each license plate is to show 3 letters, followed by 3 numbers, with no restrictions on
repeated characters or their order. The only restriction is that the letters I and 0 are
not to be used.

·         The second scheme is the same as abover, except no letter or number can appear
twice in the same license plate.

·         Under each scheme, how many different license plates can be produced?

·          Under which scheme is it more likely that there will be enough license plates?