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?

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?

You roll two fair dice. If they land with a sum of 7, you get $10. If they land with a sum of 6 or 8, you get $5. Everything else earns $0. Which of the following would be the most reasonable amount to pay to play this game?

Your business is looking into looking into three contracting firms. Based on previous research, there is a 75% chance that company 1 will earn you $40,000. There is a 45% chance that company 2 will earn you $60,000. Company 3 has a 30% chance of earning you $80,000. It costs $20,000 to draw up legal paperwork for each company. How much profit or loss would you expect after this deal is done?

• $81,000 profit

• $81,000 loss

• $21,000 profit

• $21,000 loss

Tianna works at a call center. Between 12 PM and 4 PM only 5% of her attempted calls pick up. Between 4 PM and 8 PM, 15% of her attempted calls pick up. If she expects to make 80 calls between 12 PM and 4 PM and 120 calls between 4 PM and 8 PM, how many total pick ups can she expect during her entire shift?

• Around 5

• Around 15

• Around 20

• Around 50

Your friend shuffles a standard deck of cards and says to pick one. If you pick a face card (Jack, Queen, King of each suit) your friend will give you $10. If you pick anything else, you owe your friend $5. How much should you expect to win or lose by playing this game?

• Lose $6.15

• Win $6.15

• Lose $1.50

• Win $1.50

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?

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?