Expected Value

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

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

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

• yes
• no

Answer explanation

If the result is negative you will expect to lose money.

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

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

Answer explanation

P(6) x $12 + P(1) x $6 - P(2 or 3 or 4 or 5) x $0

1/6 x $12 + 1/6 x $6 - 4/6 x $0

$2 + $1 = $3

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

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

• 85

• 83.2

• 87.1

• 84.4

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

Choose an American household at random. What is the expected number of cars for that household?

• 1.75
• 1.84
• 2.00
• 2.50

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CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household?

• 2.00
• 2.13
• 1.97
• 1.27

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

Find the expected value. READ CAREFULLY!

• 4.5
• 25.5
• 3.825
• 6.52

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

• 0.45
• 0.65
• 1.00
• 1.44

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

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 $1.54

• Win $1.50

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CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

• Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
• No, all probabilities are not be between 0 and 1 inclusive
• No, the sum of all the probabilities is not 1.
• Yes, because the distribution is symmetric

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CCSS.HSS.MD.A.1