please make sure you show all the steps and write very clear and readable.

Thank you in advance.

3) A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. Some probability calculations show the probability of getting a Bachelor of Arts and Science degree to be P(Science ? Arts) = 0.1. Given this result, we conclude that:

A. getting a Bachelor of Arts and getting a Bachelor of Science are independent.

B. getting a Bachelor of Arts and getting a Bachelor of Science are disjoint.

C. getting a Bachelor of Arts and getting a Bachelor of Science are complement.

D. getting a Bachelor of Arts and getting a Bachelor of Science are not independent.

4. We have P(A) = 0.1, P(B) = 0.3, P(A ? B) = 0. Then, events A and B:

I. are independent

II. are disjoint

III. cannot be disjoint

IV. cannot be independent

The correct answer is:

A. I only

B. II only

C. II and IV only

D. IV only

6. Let X be the room temperature of LIB 1122 at CSUDH. Then the random variable X is

A. discrete

B. continuous

7. I roll a fair die twice and obtain two numbers X1 = result of the first roll, and X2 = result of the second roll.

(a) (5 points) Find P(X1 = 2X2)9. Let A, B and C be three events in the sample space S . Suppose we know I A U B U C = S, (b) (5 points) Find P(C - (AUB))