Expected Value

You draw one card from a standard deck of playing cards. If you pick a heart, you will win $10. If you pick a face card, which is not a heart, you win $8. If you pick any other card, you lose $6. What is the expected value of the each play?

• The expected value is you win $.42, so you want to play.

• The expected value is you win $.642, so you want to play.

• The expected value is you lose $.42, so you don't want to play.

• The expected value is you lose $.142, so you don't want to play.

The world famous gambler from Philadelphia, Señor Rick, proposes the following game of chance. You roll a fair die. If you roll a 1, then Señor Rick pays you $25. If you roll a 2, Señor Rick pays you $5. If you roll a 3, you win nothing. If you roll a 4 or a 5, you must pay Señor Rick $10, and if you roll a 6, you must pay Señor Rick $15. Is Señor Rick crazy for proposing such a game?

• Señor Rick is crazy since the expected value is you win $ 1.83.

• Señor Rick is not crazy since the expected value is you loose $ .83.

• Señor Rick is not crazy since the expected value is you loose $ .83.

• Señor Rick is crazy since the expected value is you win $ -.83.

You pay $10 to play the following game of chance. There is a bag containing 12 balls, five are red, three are green and the rest are yellow. You are to draw one ball from the bag. You will win $14 if you draw a red ball and you will win $12 is you draw a yellow ball. How much do you expect to win or loss if you play this game 100 times?

• you loose $.1667

• you loose $16.67

• you win $16.67

• you win $.1667

A detective figures that he has a one in nine chance of recovering stolen property. His out-of-pocket expenses for the investigation are $9,000. If he is paid his fee only if he recovers the stolen property, what should he charge clients in order to breakeven?

• The detective must charge $81,000.

• The detective must charge $8,100

• The detective must charge $84,000

• The detective must charge $87,000

Your company plans to invest in a particular project. There is a 35% chance that you will lose $30,000, a 40% chance that you will break even, and a 25% chance that you will make $55,000. Based solely on this information, what should you do?

• You expect to make $32,500, so proceed with the project.

• You expect to lose $3,250, so do not proceed with the project.

• You expect to make $325, so proceed with the project.

• You expect to make $3,250, so proceed with the project.

A manufacturer is considering the manufacture of a new and better mousetrap. She estimates the probability that the new mousetrap is successful is 0.75. If it is successful it would generate profits of $120,000. The development costs for the mousetrap are $98,000. Should the manufacturer proceed with plans for the new mousetrap? Why or

why not?

• Expected profit of 65,000, proceed with the project.

• Expected profit of 65,500, proceed with the project.

• Expected profit of 65,600, proceed with the project.

• Expected profit of 65,700, proceed with the project.

A grab bag contains 12 packages worth 80 cents apiece, 15 packages worth 40 cents each and 25 packages worth 30 cents apiece. Is it worthwhile to pay 50 cents for the privilege of picking one of the packages at random?

• Expected value of your prize is $0.54, if you paid $0.50 then you won money.

• Expected value of your prize is $0.48, if you paid $0.50 then you lost money.

• Expected value of your prize is $0.44, if you paid $0.50 then you lost money.

• Expected value of your prize is $0.58, if you paid $0.50 then you won money.

You pay $3.00 to play. The dealer deals you one card. If it is a spade, you get $10. If it is anything else, you lose your money. Is this game fair?

• You expect to loose $.50 so not a fair game.

• You expect to loose $1.50 so not a fair game.

• You expect to win $.50 so not a fair game.

• You expect to win $1.50 so not a fair game.

A casino game costs $3.50 to play. You draw 1 card from a deck. If it is a heart, you win $10; If it is the Queen of hearts, you win $50. Is this a fair game?

• You expect to break even so it is a fair game.

• You expect to loose $.23 so it is not a fair game.

• You expect to win $.23 so it is a fair game.

• You expect to loose $.23 so it is a fair game.

A player rolls a die and receives the number of dollars equal to the number on the die EXCEPT when the die shows a 6. If a 6 is rolled, the player loses $6. If the game is to be fair, what should be the cost to play?

• The expected value is $1.7 when games costs nothing so charge $1.70 to make the game fair (expected value =0).

• The expected value is $1.6 when games costs nothing so charge $1.60 to make the game fair (expected value =0).

• The expected value is $1.5 when games costs nothing so charge $1.50 to make the game fair (expected value =0).

• The expected value is $1.4 when games costs nothing so charge $1.40 to make the game fair (expected value =0).