Expected Values

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

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. Is this a fair game?

• yes

• no

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

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14
• 4.67
• 5
• 7.5

Calculate the missing probability

• 1

• .1

• .2

• .3

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

Games of chance do not involve

• money.

• skill.

• probability.

• technology.

Number of Thunderstorms during August
Number of Storms    0     1      2      3
Probability               0.2   0.2   0.4   0.2
How many storms should we expect in August?

• 1.8
• 2.0
• 1.6
• 2.2

A child asks his parents for some money. The parents make the following offers.

Father’s offer: The child flips a coin. If the coin lands heads up, the father will give the child $20. If the coin lands tails up, the father will give the child nothing.

Mother’s offer: The child rolls a 6-sided die. The mother will give the child $3 for each dot on the up side of the die.

Which offer has the greater expected value?

(hint - create a provability model)

• mother's offer; $10.5

• father's offer; $10

• father's offer; 20$

• mother's offer; 10$

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

• yes
• no