Learn Before
Expected Payoff from a Coin Toss Gift
To illustrate the calculation of expected payoff, consider a gift from a friend that depends on a coin toss. If the gift is $20 for a win and nothing for a loss, and the coin is fair, there is a 50% probability for each outcome. The expected payoff is calculated by taking the weighted average of all possible results: . This value represents the average amount one would receive if this uncertain gift were received many times.
0
1
Tags
Library Science
Economics
Economy
Introduction to Microeconomics Course
Social Science
Empirical Science
Science
CORE Econ
Ch.4 Strategic interactions and social dilemmas - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Macroeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
Related
Proposer's Expected Payoff from an Offer
Using Expected Payoff to Decide on a Product Warranty
Expected Payoff from a Coin Toss Gift
General Calculation of Expected Payoff
A company is deciding whether to launch a new product. The marketing department provides the following analysis:
- If the launch is successful, the company will earn a profit of $5 million.
- If the launch fails, the company will incur a loss of $2 million.
- Based on market research, there is a 40% probability of success and a 60% probability of failure.
Assuming the company makes decisions based on maximizing the weighted average of all possible outcomes, what is the most rational course of action?
Investment Decision Analysis
Farmer's Planting Decision
A company is deciding between two mutually exclusive projects, Project X and Project Y. An initial analysis reveals that Project X has a significantly higher probability of success than Project Y. Based solely on this information, a rational, risk-neutral decision-maker should choose Project X to maximize their expected payoff.
A venture capitalist is evaluating four different startup investment opportunities. Match each opportunity, described by its potential outcomes and their probabilities, with its correct expected payoff.
A software company is considering adding a new feature. Market analysis suggests a 30% chance the feature will be a major success, generating $100,000 in profit; a 50% chance it will be moderately successful, generating $20,000 in profit; and a 20% chance it will fail, resulting in a loss of $40,000. The expected payoff of developing this feature is $____. (Enter a whole number without commas or dollar signs).
Critique of a Decision-Making Process
A manager needs to make a rational decision between two different investment strategies, where the final profit for each strategy is uncertain. Arrange the following steps into the correct logical sequence they should follow to determine the best strategy by comparing the weighted average of all possible results.
A firm is deciding between two mutually exclusive projects. Project A has a 70% chance of earning $10 million and a 30% chance of losing $5 million. Project B has a 40% chance of earning $20 million and a 60% chance of losing $6 million. The firm initially determines that Project A is the better choice by comparing the weighted average of all possible outcomes. Which of the following independent changes to the scenario would reverse this decision, making Project B the more rational choice?
Critique of a Business Expansion Analysis
Formula for Insurer's Expected Payoff
Learn After
Valuing a Modified Coin Toss Gift
A friend offers you a choice of a gift. You can either accept $15 for certain, or you can play a game where you roll a standard six-sided die. If the die shows a 5 or a 6, you receive $50. If it shows any other number, you receive $5. Based on a calculation of the average outcome you would expect from the game if it were played many times, which statement is the most accurate?
New Product Launch Decision
Consider a game where you draw one card from a standard 52-card deck. If you draw a heart, you win $10. If you draw any other suit, you lose $2. The statement 'The average amount you would expect to win or lose per game, if you played many times, is a positive value' is true.
Weighted Coin Game Payoff
A game involves a spinner with two equal sections. One section results in a prize of $50, and the other results in a prize of $10. Match each component of the expected payoff calculation with its correct numerical value based on this game.
You are offered a chance to play a game involving a single toss of a fair coin. If the coin lands on heads, you win $30. If it lands on tails, you lose $10. The average amount you would expect to gain or lose per game, if you were to play many times, is $____.
Investment Opportunity Evaluation
Arrange the fundamental steps for calculating the weighted average of all possible results from an uncertain event (like a game of chance) into the correct logical sequence.
A carnival game involves drawing a single ball from a bag that contains 2 green balls and 8 purple balls. Drawing a green ball wins you $50. The overall expected prize value from playing this game one time is calculated to be $18. What is the prize value for drawing a purple ball?
Investment Strategy Comparison