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

Tags

CCSS.HSS.MD.B.5A

One option in the game of roulette is to bet $6 on red. (There are 18 red compartments, 18 black compartments and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $6 you paid to play and you are awarded an additional $6. If the ball does not land on red, you win nothing and you lose your $6 bet. Find the expected payback (on average) for this game if you bet on red.

• -$5.54
• -$0.32
• -$4.48

Tags

CCSS.HSS.MD.B.5A

A child asks his parents for some money. The parents make the following offers.
 Father’s offer: The child fl ips 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 upside of the die.
Which offer has the greater expected value?

• Mother's Offer
• Father's Offer

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day.  Based on the records, X has the following probability distribution.
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is

• 0.2
• 1.4
• 2.0
• 3.0

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

John Smith is considering the purchase of a used car that has a bank book value of $16,000. He believes that there is a 20% chance that the car's transmission is damaged. If the transmission is damaged, the car would be worth only $12,000 to Smith. What is the expected value of the car to Smith?

• $16200

• $15200

• $15220

• $16220

Tags

CCSS.HSS.MD.A.2