Expected Value

You roll a standard die. You win $12 if you roll a six, $6 if you roll a one, and $0 if you roll anything else. What is the expected value of a single roll?

• $3

• $18

• $9

• $2

You spin each spinner once. You get $50 if you spin a 2 and a vowel. You get $25 if you spin a 2 and a consonant. You get $5 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game?

• $80

• $8.75

• $10.25

• $12.50

Two new movies are being released. According to market research, the first movie has an 85% chance of making $32,000,000. The second movie has a 33% chance of making $120,000,000. What is the expected earnings for these two movies?

• Around $15 million

• Around $20 million

• Around $30 million

• Around $60 million

You are going to pick a marble from the container, put it back, and take another. If you get two yellow, you win $200. If you get one yellow on either pick, you get $50. If you pick two red, you get $100. Anything else earns $0. What is the expected value of this game?

• $60

• $33.33

• $44.33

• $20

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

A company believes it has a 40% change of being successful in bidding a contract that yields a profit of $30,000. Assume it costs $5,000 in consultation fees to prepare the bid. What is the expected gain or loss for the company if it
decides to bid on the contract?

• Expected gain of $9,000

• Expected loss of $9,000

• Expected gain of $25,000

• Expected loss of $25,000

You pick a card from a deck. If you get a face card (12/52), you win $5. If you get an ace (4/52), you win $30. For any other card (26/52), you win nothing. Find the expected value you will win.

• $5.00

• $3.55

• $4.04

• $3.46

An insurance company charges $150 for a policy that will pay for at most one accident. For a major accident, the policy pays $5000; for a minor accident, the policy pays $1000. The $150 premium is not returned. • The company estimates that the probability of a major accident is 0.005, and the probability of a minor one is 0.08. • What is the expected value of the policy to the insurance company?

• 150

• 45

• 55

• 75

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

• 220

• 239

• 261

• 309

• 320

A mysterious card-playing squirrel (pictured) offers you the opportunity to join in his game.

The rules are:

- To play you must pay him $2

- If you pick a spade from a shuffled deck, you win $9.

Find the expected value you win (or lose) per game.

• Win $0.25

• Win $2.25

• Lose $0.25

• Lose $2.25