### MATH 113: Introduction to Probability

Name:
1. A six sided die is rolled. What is the sample space S for this experiment?

2. Events E1, E2, E3 and E4 are defined as follows:

E1: the number rolled is odd.
E2: the number rolled is even.
E3: the number rolled is a multiple of 3.
E4: the number rolled is greater than 3.

a) What subset of S describes each event?

b) Are events E1 and E2 mutually exclusive? Why or why not?

c) Are events E2 and E3 mutually exclusive? Why or why not?

d) Are events E3 and E4 mutually exclusive? Why or why not?

e) Are events E4 and E1 mutually exclusive? Why or why not?

3. Suppose that we compute the following probabilities for these experiments:

P(E1) = .5
P(E2) = .5
P(E3) = .34
P(E4) = .5
P(E1 and E2) = 0
P(E2 and E3) = .17
P(E3 and E4) = .17
P(E4 and E1) = .17

Events A and B are independent when P(A and B) equals P(A) * P(B). Use this fact to answer the following questions. Show your work.

a) Are events E1 and E2 independent?

b) Are events E2 and E3 independent?

c) Are events E3 and E4 independent?

d) Are events E4 and E1 independent?