Making Decisions with Expected Values

You are considering buying a lottery ticket for $10 that has a 1% chance of winning $800. Should you buy it?

• Yes, the expected value is $2.00

• Yes, the expected value is $1.90

• No, the expected value is -$2.00

• No, the expected value is -$1.90

Tags

CCSS.HSS.MD.B.5B

A box of old baseball cards costs $20. The card seller says there may be valuable cards within the box; he advertises the following probability distribution of potential card values (NOT your overall net gain). Should you buy the box of cards?

• Yes; the expected value is $1.00

• Yes; the expected value is $19.00

• No; the expected value is -$1.00

• No; the expected value is -$12.00

Tags

CCSS.HSS.MD.B.5B

Why can expected value be used to make decisions?

• For each trial, you are most likely to gain/lose the exact expected value.

• For each trial, you have a 50% chance of winning more than the expected value.

• Over many trials, your total net gain/loss will be equal to the expected value.

• Over many trials, your average net gain/loss will be around the expected value.

Tags

CCSS.HSS.MD.B.5B

A card is drawn from a fair, standard deck of cards (with replacement). If it is a diamond, you win $120. If it is a heart, you win $60. If it is anything else, you lose $100. Previous results from this deck are provided. Use empirical or theoretical probabilities to determine whether you should play this game.

• Yes; using theoretical probability, your expected value is $25.00.

• Yes; using empirical probability, your expected value is $25.00.

• No; using theoretical probability, your expected value is -$5.00.

• No; using empirical probability, your expected value is -$5.00.

Tags

CCSS.HSS.MD.B.5A

A weighted, unfair coin is flipped twice. If both flips are heads, you win $50. If both flips are tails, you lose $80. If one is heads and one is tails, you lose $5. Previous results show the coin lands on heads about 60% of the time. Use empirical or theoretical probabilities to determine whether you should play this game.

• Yes; using theoretical probability, your expected value is $2.80

• Yes; using empirical probability, your expected value is $2.80

• No; using theoretical probability, your expected value is -$10.00

• No; using empirical probability, your expected value is -$10.00

Tags

CCSS.HSS.MD.B.5B

Freddie needs to choose between two car insurance plans. He has created the following probability distributions of the potential costs of each plan based on his estimated probability of getting into a major accident, minor accident, or no accident. Which plan should he choose to minimize his cost, and why?

• Plan Y; the expected value is $1.60 higher

• Plan Y; the expected value is $1.60 lower

• Plan X; the expected value is $1.60 higher

• Plan X; the expected value is $1.60 lower

• Either one; the expected values are equal

Tags

CCSS.HSS.MD.B.5B

You have taken a great selfie and are debating whether to post it on your main account or your alternate account. Based on previous posts, you have created the following probability distributions of the potential likes on each account. Which account should you post the selfie on to maximize the number of likes, and why?

• Main Account; the expected value is 2.5 likes higher

• Main Account; the expected value is 4.5 likes higher

• Alternate Account; the expected value is 2.5 likes higher

• Alternate Account; the expected value is 4.5 likes higher

• Either one; the expected values are equal

Tags

CCSS.HSS.MD.B.5B

You have been offered two jobs waiting on tables at different restaurants. By analyzing the probability distribution of tips (per day) at each job, you have determined one job has a $2 higher expected value than the other job. So, you choose that job. Which of the following is the best reasoning for your decision?

• Every hour, you will make about $2 more in tips.

• Every day, you will make $2 more in tips.

• Over several days, you will make an average of $2 more in tips each day.

• Over several days, you will make a total of $2 more in tips.

Tags

CCSS.HSS.MD.B.5B

A basketball coach is choosing between four players for the last spot on the team. He has estimated their probability distribution of points scored. Which player should he choose to maximize points scored?

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Tags

CCSS.HSS.MD.B.5B

There are 20 students in a Geography class and 30 students in a History class. Five students are randomly selected from each class to participate in a survey. Is this a fair decision? Why or why not?

• Yes; all students have an equal chance of being selected

• No; students in the Geography class have a lower probability of being selected

• No; students in the History class have a lower probability of being selected

• Not Enough Info

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7