Expected Value and Fair Games

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

Tags

CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.B.5

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

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.7

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

An insurance company charges $150 for a policy that will pay for at most one accident. For a major accident, the policy pays $5000; for a minor accident, the policy pays $1000. The $150 premium is not returned. • The company estimates that the probability of a major accident is 0.005, and the probability of a minor one is 0.08. • What is the expected value of the policy to the insurance company?

• 150

• 45

• 55

• 75

Tags

CCSS.HSS.MD.B.5A

In a state lottery, a single digit is drawn from each of four containers. Each container has 10 balls numbered 0 through 9. To play, you choose a 4-digit number and pay $1. If your number is drawn, you win $5000. If your number is not drawn, you lose your dollar. What is the expected value for this game?

• You are expected to lose 1 dollar each time you play.

• You are expected to lose 50 cents each time you play.

• You are expected to win 1 dollar each time you play.

• You are expected to lose 75 cents each time you play.

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 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$

Tags

CCSS.HSS.MD.B.5B

Your company is considering developing one of two cell phones. Your development and market research teams provide you with the following projections. Cell phone A: Cost of development: $2,500,000 Projected sales: 50% chance of net sales of $5,000,000 30% chance of net sales of $3,000,000 20% chance of net sales of $1,500,000 Cell phone B: Cost of development: $1,500,000 Projected sales: 30% chance of net sales of $4,000,000 60% chance of net sales of $2,000,000 10% chance of net sales of $500,000.

Which phone should they go with based on the tree diagram above?

• cellphone A; 1.2 million expected value

• cellphone B; 1 million expected value

• cellphone B, it has lower probability of losing a million