HELP me to answer each of the following:

1. Let S = {x, y, z}; find all the events of this experiment.

2. Let S = {v, x, y, z}; find all the events of this experiment.

3. Let S be a sample space of an experiment with n outcomes. Determine the number

of the events of this experiment.

4. Let S = {5, 10, 15, 20, 25, 30} be the sample space of an experiment and let T = {5,

10}, V = { 5, 20, 30}, and W = {10, 15, 25} be the events of the experiment.

a. Find T V and T V.

b. Find V W and V W.

c. Find Wc

d. Are T and V mutually exclusive? T and W? V and W?

e. Are T V and Tc Vc mutually exclusive?

5. Let S = {a, b, c, d, e} , X = {a, c, e}, Y = {b, d}, Z = {d, e},

a. Find the event X Y Z.

a. Find the event X Y Z.

6. In a show, the winner is asked to select two prizes from five different prizes A, B, C, D,

and E.

a. Describe the sample space of the possible outcomes.

b. How many events are there corresponding to a selection that includes A?

List all the events.

c. How many events are there corresponding to a selection that is include A

and B? List all the events.

d. How many events are there corresponding to a selection that includes either

A or B? List all the events.

7. A committee of three is randomly chosen from five students denoted by S1, S2, S3, S4,

and S5.

a. List the sample space are both in the committees of three.

b. List all the events of this sample space for which

i. S1 and S2 are both in the committee.

ii. S1 or S2 in the committee.

iii. S1 and S3 are both in the committee.

iv. S5 is in the committee.