LT 1c Expected Value

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. What is the expected amount you win?

• $0.00

• -$1.00

• $1.00

• $3.00

Answer explanation

You find the probability of a 2 or a 4 (2/6) and multiply by the amount you would win ($3- the $1 you paid to play). Then you find the probability you won't win (4/6) and multiply by the amount you lose ($1 that you paid to play). In this case it comes out to be $0

Tags

CCSS.HSS.MD.B.5A

If the expected value is negative, are you expected to win?

• yes
• no

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CCSS.HSS.MD.A.2

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?

• $1

• $0.50

• -$0.50

• $0

Answer explanation

The probability of flipping and getting heads is 1/2 multiplied by the amount you win and then it's also 1/2 for landing on tails and losing $3

Tags

CCSS.HSS.MD.B.5A

Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. What are your expected winnings (on average)?

• $800 
• -$6.50
• -$6
• -$5.20

Answer explanation

SInce the cost of the ticket is $6, that needs to be subtracted from the winning value. There's only 1 winning ticket which means all the other tickets are losing and they lose their $6

Tags

CCSS.HSS.MD.B.5A

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average)? How much?

• lose an average of $5.50

• lose an average of $1.50

• win an average of $2.00

• lose an average of $10.00

Answer explanation

Since they paid $2, each winning value is $2 less and the 493 is all the people who don't win any prize. They just lose their $2.

Tags

CCSS.HSS.MD.B.5A

A $20 bill, two $10 bills, three $5 bills and four $1 bills are placed in a bag. If a bill is chosen at random, what is the expected value for the amount you will win when you chose one bill from the bag?

• $5.90

• $9.00

• $7.50

• $10.00

Answer explanation

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CCSS.HSS.MD.B.5A

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

Answer explanation

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CCSS.HSS.MD.B.5A

A raffle is held by the MTHS ASB to draw for a $1000 plasma television. Two thousand tickets are sold at $1.00 each. Find the expected value for one ticket.

• Lose $0.50

• Win $0.50

• Lose $5

• Win $5

Answer explanation

Again, the cost of the ticket ($1) needs to be subtracted from the value of the tv. There's only one winning ticket so the rest of the 1,999 people lose $1

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CCSS.HSS.MD.B.5A

A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of a blue pays $5.00. A roll of a green pays $2.00. The charge to play the game is $2.00. Would you play the game? Why or why not?

• No, you expect to lose $0.50

• Yes, you expect to win $0.50

Answer explanation

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CCSS.HSS.MD.B.5A

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

Answer explanation

The key word here is "profit". Profit means you've already subtracted out your loss and the $30000 is exactly what you would earn if you get it. The $5000 is only lost if they lose the bid.

Tags

CCSS.HSS.MD.B.5A