Expected Value Answers

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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.

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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)

Which statement below correctly depicts the expected value of a fair game?

E(X) = 0

E(X) = 1

E(X) > 0

E(X) >1

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

The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lunch each day. What is the expected value for a student to spend on lunch each day? Student Lunch SurveyNumber of StudentsDollars Spent on Lunch Each Day2 $101$812$623$58$44$3

$2.59

$5.11

$5.18

$9.07

Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll?

Negative two-thirds

Negative one-sixth

one-sixth

Two-thirds

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

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.

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

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Expected Value Answers

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