When answering please use the same alphabet as the questions.

8. (30 points) You are going to draw the top card from a shuffled deck. The following events are defined:

Event A: draw a diamond

Event B: draw a spade

Event C: draw a heart

Event D: draw a club

Event E: draw a jack

Event F: draw a face card

Event G: draw a 5

Event H: draw a 5 of diamonds

Answer the following questions. You may leave all answers as unreduced fractions.

a. How many possible outcomes are there for the top card? In other words, what is the size of the sample space?

b. Are events A and B mutually exclusive? Circle the correct answer below.

YES NO NOT ENOUGH INFO

C. Are events A and B exhaustive? Circle the correct answer below.

YES NO NOT ENOUGH INFO.

D. Are events G and H mutually exclusive? Circle the correct answer below.

YES NO

E. Are events G and H exhaustive? Circle the correct answer below.

YES NO

f. What is P(A)?

g. What is P(B)?

h. What is P(C)?

i. What is P(D)?

j. What is P(E)?

k. What is P(F)?

i. What is P(G)?

m. What is P(H)?

n. Explain why P(A) = P(B) = P(C) = P(D). You should refer to the outcomes of the experiment that make A, B, C, and D true in this explanation.

o. Explain why P(G) > P(H). Again, refer to the outcomes that make each event true.

p. What is P(A C)?

q. What is P(A U C)?

r. What is P(A E)?

s. What is P(A U E)?

t. What is P(A G)?

u. What is P(A U G)?

v. Explain why P(A G) = P(H). Again, refer to the outcomes that make each event true.