Expected Value Answers

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Two students devised a game called “3 Pennies & 2 Nickels.” Each player will choose to play the pennies or the nickels. In each round, the players will flip all their coins on the table and record how many heads and tails they have. The table below includes the point scheme.Point Values for “3 Pennies & 2 Nickels”Penny PointsNickel PointsAll pennies heads: –2Both nickels heads: –2At least one of each: +3One of each: +5All pennies tails: –2Both nickels tails: –2Alyssa wants to play the game. Choose the statement below that is correct in all aspects.

E(penny) = –0.33 and E(nickel) = 0.33, so she should play with the nickels.

E(penny) = 0.5 and E(nickel) = 1.5, so she should play with the nickels.

E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.

E(penny) = 2.38 and E(nickel) = 2, so she should play with the pennies.

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A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

30,000 (StartFraction 1 Over 5,000 EndFraction) + 100 (StartFraction 1 Over 1000 EndFraction) + (negative 20) (StartFraction 2497 Over 2500 EndFraction) = E (X)

29,980 (StartFraction 1 Over 5,000 EndFraction) + 80 (StartFraction 1 Over 1000 EndFraction) + (negative 20) (StartFraction 2497 Over 2500 EndFraction) = E (X)

30,000 (StartFraction 1 Over 5,000 EndFraction) + 100 (StartFraction 1 Over 1000 EndFraction) = E (X)

29,980 (StartFraction 1 Over 5,000 EndFraction) + 80 (StartFraction 1 Over 1000 EndFraction) = E (X)

Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

The odd numbered regions will add one point. The even numbered regions lose one point.

Red will add one point. Any other color will lose one point.

A number less than or equal to 3 will add one point.A 4 will lose two points.

Odds will add a point value equal to the number on the space.Evens will lose a point value equal to the number on the space.

If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?

100 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)

95 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)

(100 minus 5) (StartFraction 1 Over 500 EndFraction) = E (X)

(100) (StartFraction 1 Over 500 EndFraction) = E (X)

Sebastian has researched the following scoring schemes: one that has 5 question choices, one that has 4 question choices, and two that have 3 question choices. Which scoring scheme is the most favorable to the test taker?Scoring Schemes of Multiple-Choice TestsScoring SchemePoints for Correct AnswerPoints for Incorrect AnswerA (5 choices)1B (3 choices)2C (4 choices)1D (3 choices)3

scheme A

scheme B

scheme C

scheme D

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament?

–$800

–$200

$2,600

$3,400

A business has an opportunity to invest $35,000. If the investment is a success, the business earns a profit of $150,000. Otherwise, the investment will result in a total loss of all monies. If the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?

0.27(150,000) + 0.73(–35,000) = E(X)

150,000 – 0.73(35,000) = E(X)

0.27(150,000 – 35,000) = E(X)

0.27(115,000) + 0.73(–35,000) = E(X)

A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are $100 each, what is the profit per item?

loss of $15.10

loss of $15

profit of $2.90

profit of $3.00

An investor has an opportunity to invest in three companies. She researched each company and collected the information in the table below. Which company would provide the best investment?Probability of Profit and Loss by CompanyCompanyLoss, Probability of LossProbability to Break EvenProfit, Probability of ProfitA$24,000, 16%50%$10,000, 34%B$12,000, 32%40%$21,000, 28%C$6,000, 23%17%$5,000, 60%

company A

company B

company C

All companies have a probability of loss.

Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?

It is a fair game.

It is a favorable game.

It is unfavorable game.

Johnny cannot determine whether the game is fair without knowing the rules.

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Expected Value Answers

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