1.

You toss a pair of fair dice. If the sum of the numbers shown on the faces of the dice is 9 or more, you win $100. If the sum is 7 or 8 you neither win nor lose. If the sum is 6 or less, you lose $70. You pay $5 to play the game. Find the player's expected value of the game. Round your answer to the nearest dollars.

2.

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

c. Are B and D independent?

d. Are B and D mutually exclusive?

3.

In a bookstore, the probability that the customer buys a novel is 0.6, and the probability that the customer buys a non-fiction book is 0.4. Suppose that the probability that the customer buys both is 0.2.

a. Draw a Venn diagram representing the situation.

b. Find the probability that the customer buys either a novel or anon-fiction book.

c. In the Venn diagram, describe the overlapping area using a complete sentence.

d. Suppose that some customers buy only compact disks. Draw an oval in your Venn diagram representing this event.

4.

A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.

a. List the sample space.

b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A).

c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and

B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.

d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and

C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.