AQR (6): Expected Value and Payoff

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

• yes
• no

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?

• $12.50
• $5
• $7.50
• $10

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

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

• 85

• 83.2

• 87.1

• 84.4

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

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

• 1.75
• 1.84
• 2.00
• 2.50

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

• 0.45
• 0.65
• 1.00
• 1.44

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

A car dealer buys hybrids for $21,000 each and sells them for $24,500 each. Find his expected weekly profit.

• $2,380
• $5,355
• $8,109
• $37,485