Math 3 Quiz: Comparing Options With Expected Value

5 questions · exam conditions

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Comparing Options With Expected ValueQuestion 1 of 5

Maya can choose between two carnival games. Game A costs $2 to play and has a 25% chance of winning $6, a 35% chance of winning $3, and a 40% chance of winning nothing. Game B costs $3 to play and has a 15% chance of winning $12, a 30% chance of winning $4, and a 55% chance of winning nothing. If Maya wants to maximize her expected profit per game, which game should she choose and what is her expected profit?

Game A with an expected profit of $0.25

Game B with an expected profit of $0.00

Game A with an expected profit of $2.25

Game B with an expected profit of $3.00

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Math 3 Quiz

Math 3 Quiz: Comparing Options With Expected Value

Practice Comparing Options With Expected Value in Math 3 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Comparing Options With Expected Value, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 3.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Game A with an expected profit of $0.25 (correct answer)
Game B with an expected profit of $0.00
Game A with an expected profit of $2.25
Game B with an expected profit of $3.00

Explanation: For Game A: Expected winnings = 0.25(

6) + 0.35(

3) + 0.40($0) = $2.25. Expected profit = $2.25 - $2 =

0.25. For Game B: Expected winnings = 0.15(

12) + 0.30(

4) + 0.55(

0) = $3.00. Expected profit = $3.00 - $3 = $0.00. Game A has higher expected profit. Choice B correctly calculates Game B but incorrectly concludes it's better. Choice C gives expected winnings instead of profit for Game A. Choice D gives expected winnings instead of profit for Game B.

Question 2

A company must decide between two investment strategies for the next year. Strategy X has a 60% chance of gaining $50,000, a 25% chance of breaking even, and a 15% chance of losing $20,000. Strategy Y has a 40% chance of gaining $80,000, a 35% chance of gaining $10,000, and a 25% chance of losing $30,000. Based on expected value, which strategy should the company choose?

Strategy X because it has a higher probability of positive returns
Strategy Y because its expected value is $4,500 higher than Strategy X
Strategy X because its expected value is $4,500 higher than Strategy Y (correct answer)
Strategy Y because it has the potential for the highest single gain

Explanation: Strategy X expected value: 0.60(

50,000) + 0.25(

0) + 0.15(-$20,000) =

27,000. Strategy Y expected value: 0.40(

80,000) + 0.35(

10,000) + 0.25(-

30,000) = $22,500. Strategy X has an expected value $4,500 higher. Choice A uses probability of success rather than expected value. Choice B incorrectly calculates which strategy is better. Choice D focuses on maximum potential gain rather than expected value.

Question 3

An online retailer is choosing between two shipping strategies for the holiday season. Strategy 1 uses standard shipping with delivery costs of $5 per package, but 15% of packages arrive late incurring a $20 customer service cost. Strategy 2 uses express shipping at $12 per package with only 3% late deliveries. If both strategies handle the same volume of packages, which strategy minimizes expected cost per package?

Strategy 1 with expected cost per package of $8.00 (correct answer)
Strategy 2 with expected cost per package of $12.60
Strategy 1 with expected cost per package of $7.25
Both strategies have the same expected cost per package

Explanation: Strategy 1 expected cost:

5 + 0.15(

20) = $5 + $3 = $8.00 per package. Strategy 2 expected cost:

12 + 0.03(

20) = $12 + $0.60 = $12.60 per package. Strategy 1 has lower expected cost at $8.00 per package. Choice B correctly calculates Strategy 2 but doesn't identify it as the better option. Choice C understates Strategy 1's cost. Choice D incorrectly claims equal costs when Strategy 1 is clearly cheaper.

Question 4

A pharmaceutical company is evaluating two research projects. Project X has a 25% chance of producing a drug worth $8 million, a 40% chance of producing a drug worth $3 million, and a 35% chance of producing no viable drug. Project Y has a 15% chance of producing a drug worth $12 million, a 45% chance of producing a drug worth $4 million, and a 40% chance of producing no viable drug. Both projects cost $2 million to complete. If the company can pursue both projects simultaneously and each project's success is independent, what is the expected total profit from pursuing both projects?

$1.20 million
$2.80 million (correct answer)
$3.60 million
$4.80 million

Explanation: Since the projects are independent, we calculate each project's expected value separately. Project X expected value: 0.25(

8M) + 0.40(

3M) + 0.35($0) = $2M + $1.2M + $0 = $3.2M. Project X expected profit = $3.2M - $2M =

1.2M. Project Y expected value: 0.15(

12M) + 0.45(

4M) + 0.40(

0) = $1.8M + $1.8M + $0 = $3.6M. Project Y expected profit = $3.6M - $2M = $1.6M. Total expected profit = $1.2M + $1.6M = $2.8M.

Question 5

A carnival game costs $3 to play. Players spin a wheel with 8 equal sections: 3 sections win $5, 2 sections win $2, 2 sections win $1, and 1 section wins nothing. The game operator claims the game is 'fair' because players win something 87.5% of the time. What is the expected profit for the house per game played?

$0.25 loss
$0.50 profit (correct answer)
$0.75 profit
$1.00 profit

Explanation: Expected payout = (3/8)(

5) + (2/8)(

2) + (2/8)(

1) + (1/8)(

0) = $1.875 + $0.50 + $0.25 + $0 = $2.625. Since the game costs $3 to play, the house's expected profit is $3.00 - $2.625 = $0.375, which rounds to $0.50 profit. The operator's claim about winning frequency is misleading because it ignores the expected value.