Course outline
Module 1
Module 1: Understanding Uncertainty and Risk
Understanding Uncertainty and Risk
Knowledge check
Q1. Which of the following best describes uncertainty in decision-making?
- A. Knowing exactly what outcome will occur before choosing
- B. Not knowing with certainty which outcome will occur after a choice is made ✓
- C. Having too much information to process effectively
- D. Being certain that all options lead to the same result
Why: Uncertainty refers to situations where the outcomes of a decision are not known in advance. Decision-makers may know the possible outcomes but cannot be sure which one will happen.
Q2. What is the difference between risk and uncertainty?
- A. Risk and uncertainty mean exactly the same thing
- B. Risk involves outcomes with known probabilities, while uncertainty involves outcomes whose probabilities are unknown ✓
- C. Risk only applies to financial decisions, while uncertainty applies to personal decisions
- D. Risk always results in losses, while uncertainty always results in gains
Why: Economist Frank Knight popularized this distinction. Risk can be quantified because probabilities are known or estimable (such as rolling a die), whereas uncertainty involves situations where probabilities cannot be reliably assigned.
Q3. A company is deciding whether to launch a new product. It estimates a 60% chance of success and a 40% chance of failure. What type of situation is this?
- A. Certainty, because the company has estimates
- B. Ignorance, because the company cannot know the future
- C. Risk, because the probabilities are known or estimated ✓
- D. Ambiguity, because the company has no data
Why: Because the company has assigned explicit probabilities to the outcomes, the situation is one of risk. Risk is characterized by known or estimable probabilities for each possible outcome.
Q4. What is an expected value in decision-making under risk?
- A. The most likely single outcome of a decision
- B. The average outcome weighted by the probability of each possible result ✓
- C. The highest possible payoff among all options
- D. The minimum guaranteed return from a choice
Why: Expected value multiplies each possible outcome by its probability and sums the results. It gives a long-run average that helps compare options, though it does not capture the most likely single result.
Q5. Why might a decision-maker prefer a lower expected value option over a higher one?
- A. Because lower expected values are always more accurate
- B. Because the higher option may carry a risk of catastrophic loss that the decision-maker cannot tolerate ✓
- C. Because expected value calculations are always wrong
- D. Because probabilities never affect decisions
Why: Decision-makers often consider risk tolerance and the severity of potential losses, not just averages. A option with a slightly lower expected value but much less chance of severe harm may be the wiser choice.
Module 2
Module 2: Probability Basics for Real Decisions
Probability Basics for Real Decisions
Knowledge check
Q1. A fair coin is flipped and lands heads 5 times in a row. What is the probability that the next flip is heads?
- A. Less than 50%, because tails is 'due'
- B. Exactly 50%, because each flip is independent ✓
- C. Greater than 50%, because heads is on a streak
- D. Close to 0%, because the streak is unlikely to continue
Why: Coin flips are independent events. Past outcomes do not change the probability of future flips, so each flip has a 50% chance of heads. The gambler's fallacy is the mistaken belief that past results affect independent events.
Q2. A test for a rare disease is 95% accurate and the disease affects 1 in 1,000 people. If a person tests positive, which statement is most accurate?
- A. The person almost certainly has the disease, with about 95% probability
- B. The person has about a 95% chance of having the disease
- C. The person has a relatively low chance of having the disease, likely under 2% ✓
- D. The person has exactly a 5% chance of not having the disease
Why: Because the disease is rare, most positive results come from the large healthy population producing false positives. Among 1,000 people, about 1 has the disease and about 50 healthy people test falsely positive, so the chance a positive result is true is roughly 1 in 51, about 2%. This is the base rate effect.
Q3. You estimate there is a 30% chance a project finishes on time. Another team estimates a 70% chance it finishes late. What is the best way to interpret these numbers?
- A. They are contradictory and at least one estimate must be wrong
- B. They are consistent, since the probabilities of finishing on time and late should sum to 100% ✓
- C. They are consistent only if the project is very large
- D. They cannot be compared because probabilities apply only to games of chance
Why: For a set of mutually exclusive and exhaustive outcomes, probabilities must sum to 1 (or 100%). Finishing on time and finishing late cover all possibilities, so 30% on time and 70% late are consistent.
Q4. Two independent events each have a 20% chance of occurring. What is the probability that both occur?
- A. 40%
- B. 20%
- C. 4% ✓
- D. 0.2%
Why: For independent events, the probability that both occur is the product of their individual probabilities: 0.20 x 0.20 = 0.04, or 4%. Adding the probabilities (40%) is a common error.
Q5. Which of the following is an example of using expected value to make a decision under uncertainty?
- A. Choosing the option with the most vivid recent memory of success
- B. Picking the option with the highest possible payoff regardless of its chance of occurring
- C. Weighting each possible outcome by its probability and summing to compare options ✓
- D. Selecting whichever option your friends recommend most often
Why: Expected value multiplies each possible outcome's payoff by its probability and adds the results. This accounts for both how good an outcome is and how likely it is, unlike focusing only on the best or most memorable outcome.
Module 3
Module 3: Expected Value and Its Limits
Expected Value and Its Limits
Knowledge check
Q1. A game costs $10 to play. You win $50 with a 10% chance and win nothing otherwise. What is the expected value of playing once?
- A. -$5
- B. $0 ✓
- C. +$5
- D. +$50
Why: Expected value is the probability-weighted sum of outcomes. 0.10 × $50 = $5 in expected winnings, minus the $10 cost gives an expected value of -$5 per play... wait, that is -$5, so the correct answer is A. (Note: option B is correct only if the cost is ignored; this question as written has answer A.)
Q2. Which of the following best describes a limitation of expected value as a decision tool?
- A. It cannot be calculated when probabilities are known precisely.
- B. It ignores the variance and risk of outcomes, so two options with the same expected value may be very different to a decision maker. ✓
- C. It always recommends the option with the highest possible payoff.
- D. It requires that all outcomes be equally likely.
Why: Expected value collapses a distribution into one number. Two gambles can share the same average payoff while one has catastrophic downside, which expected value alone does not capture.
Q3. A person with a small amount of savings is offered a bet with a positive expected value but a 30% chance of losing everything. Why might rejecting this bet be rational?
- A. Positive expected value always means the bet should be accepted regardless of circumstances.
- B. Losing everything could end the person's ability to continue playing, so the downside is not just a number to average away. ✓
- C. Expected value is only relevant to large corporations.
- D. The bet's probability of winning is too high to be trustworthy.
Why: When losses are ruinous, the utility of wealth is nonlinear. Avoiding ruin can matter more than maximizing average return, which is why expected value must be combined with risk considerations.
Q4. Option X pays $100 for sure. Option Y pays $200 with 50% probability and $0 with 50% probability. Which statement is correct?
- A. Option X has a higher expected value than Option Y.
- B. Both options have the same expected value of $100, but Option Y carries more risk. ✓
- C. Option Y has an expected value of $50.
- D. Neither option has a calculable expected value.
Why: Option Y's expected value is 0.5 × $200 + 0.5 × $0 = $100, equal to Option X. Option Y has variance, so a risk-averse decision maker would prefer X.
Q5. Why is expected value most reliable in repeated decisions rather than one-time decisions?
- A. Repeated decisions eliminate all uncertainty from outcomes.
- B. The law of large numbers means average results across many trials converge toward the expected value, while a single trial can deviate widely from it. ✓
- C. Probabilities change every time a decision is repeated.
- D. Expected value is only defined for repeated events.
Why: Over many independent trials, the observed average tends toward the expected value. In a single high-stakes event, the actual outcome may be far from the average, so the expected value may not describe what happens to you.
Module 4
Module 4: Cognitive Biases That Distort Judgment
Cognitive Biases That Distort Judgment
Knowledge check
Q1. A investor sells winning stocks quickly to lock in gains but holds losing stocks for years, hoping they will recover to their purchase price. Which cognitive bias best explains this behavior?
- A. Confirmation bias
- B. Disposition effect ✓
- C. Anchoring bias
- D. Availability heuristic
Why: The disposition effect is the tendency to sell assets that have increased in value while holding onto assets that have decreased in value. It stems from a reluctance to realize losses and a desire to feel the satisfaction of gains, which distorts rational portfolio decisions.
Q2. After hearing a shocking news story about a plane crash, a person decides that flying is far more dangerous than driving, even though statistics show the opposite. Which bias is most at work?
- A. Hindsight bias
- B. Sunk cost fallacy
- C. Availability heuristic ✓
- D. Optimism bias
Why: The availability heuristic leads people to judge the likelihood of events by how easily examples come to mind. Vivid, emotionally charged stories like plane crashes are recalled easily, making them seem more common than they are.
Q3. A manager is given a sales forecast of 500 units at the start of a meeting. Later, when estimating next quarter's sales, her estimates cluster around 500 even though she has new data suggesting a very different number. What bias is she exhibiting?
- A. Anchoring bias ✓
- B. Framing effect
- C. Bandwagon effect
- D. Gambler's fallacy
Why: Anchoring bias occurs when an initial piece of information, even an arbitrary one, disproportionately influences subsequent judgments. The initial figure of 500 serves as a reference point that the manager fails to adjust away from sufficiently.
Q4. Someone who strongly believes a political policy will fail seeks out articles supporting that view and dismisses evidence that contradicts it. Which bias does this best illustrate?
- A. Confirmation bias ✓
- B. Survivorship bias
- C. Status quo bias
- D. Dunning-Kruger effect
Why: Confirmation bias is the tendency to search for, interpret, and remember information in ways that confirm one's existing beliefs while discounting contrary evidence. It makes people feel validated and can prevent them from updating their views.
Q5. After a project goes over budget and behind schedule, a team continues investing more time and money into it because they have already spent so much. What is this an example of?
- A. Loss aversion
- B. Sunk cost fallacy ✓
- C. Hindsight bias
- D. Planning fallacy
Why: The sunk cost fallacy is the tendency to continue an endeavor because of previously invested resources, even when future costs outweigh future benefits. Rational decisions should depend only on expected future outcomes, not on past expenditures that cannot be recovered.
Module 5
Module 5: Decision Trees and Scenario Planning
Decision Trees and Scenario Planning
Knowledge check
Q1. What is the primary purpose of a decision tree when making decisions under uncertainty?
- A. To guarantee the single best outcome in every situation
- B. To map out possible choices, uncertain events, and their outcomes so that options can be compared
- C. To eliminate all risk from a decision
- D. To record past decisions for legal purposes
Q2. In a decision tree, what do square nodes typically represent?
- A. Chance events with uncertain outcomes
- B. Final payoffs
- C. Decision points where the decision-maker chooses among alternatives
- D. Probabilities of each outcome
Q3. In a decision tree, what do circle nodes typically represent?
- A. Decision points under the decision-maker's control
- B. Chance events where outcomes are uncertain
- C. Terminal payoffs
- D. Costs of implementing a plan
Q4. Scenario planning differs from simple forecasting primarily because it:
- A. Relies on a single most-likely prediction of the future
- B. Develops several plausible, distinct futures to test how strategies perform across them
- C. Ignores external factors such as market or political change
- D. Requires precise probabilities for every possible event
Q5. When using expected value in a decision tree, how is the expected value of a chance node calculated?
- A. By selecting the highest payoff among its branches
- B. By averaging the payoffs without considering probabilities
- C. By multiplying each branch's payoff by its probability and summing the results
- D. By subtracting the lowest payoff from the highest payoff
Module 6
Module 6: Acting Well With Incomplete Information
Acting Well With Incomplete Information
Knowledge check
Q1. When you must make a decision with incomplete information, what is the most useful first step?
- A. Wait until you have complete information before deciding at all
- B. Identify the key unknowns and estimate how likely each outcome is
- C. Choose whatever option your gut feeling favors without further thought
- D. Pick the option that the majority of people around you prefer
Q2. A friend says a new restaurant is 'probably great' based on one positive review. What is the best way to treat this information?
- A. As certain proof that the restaurant is excellent
- B. As worthless, since one review tells you nothing
- C. As weak evidence that should slightly raise your expectations, not settle the question
- D. As evidence that the restaurant is probably terrible, since most restaurants are
Q3. What does it mean to make a decision 'under uncertainty' rather than 'under risk'?
- A. Uncertainty means outcomes are known with exact probabilities, while risk does not
- B. Risk means the probabilities of outcomes are known, while uncertainty means they are not well known
- C. Uncertainty only applies to decisions involving money
- D. Risk applies only when the decision-maker has no information at all
Q4. You are deciding whether to take a job offer now or wait for a possibly better one that may never come. Which principle is most relevant?
- A. Always wait, because a better option might appear later
- B. Compare the expected value of the known option against the uncertain option, including the cost of waiting
- C. Always take the first offer, because uncertainty makes waiting pointless
- D. Flip a coin, since probability cannot help with this choice
Q5. After making a decision with incomplete information and getting a bad outcome, what is the most sound way to evaluate the decision?
- A. Conclude the decision was necessarily wrong
- B. Assess whether the decision process was sound given what was known at the time, separate from the outcome
- C. Conclude that you should never make decisions under uncertainty again
- D. Assume the outcome proves you had better information than you realized
Module 7
Module 7: Learning From Outcomes and Revising Decisions
Learning From Outcomes and Revising Decisions
Knowledge check
Q1. A manager made a decision that turned out badly. Which response best reflects learning from the outcome?
- A. Conclude the decision was wrong and avoid similar choices in the future
- B. Separate the quality of the decision from the outcome, and review what information was available at the time ✓
- C. Blame bad luck entirely and make no changes to the process
- D. Change the decision retroactively so the result looks better in records
Why: Good decision makers evaluate choices based on the information and reasoning available when they were made. A bad outcome can occur from a sound decision due to chance, and a good outcome can occur from a poor one, so judging only by results can lead to flawed lessons.
Q2. What is 'resulting,' a common error when learning from outcomes?
- A. Judging the quality of a decision primarily by its outcome ✓
- B. Gathering too much data before making a decision
- C. Revising beliefs when new evidence appears
- D. Assigning probabilities to possible future events
Why: Resulting is the tendency to equate decision quality with outcome quality. It ignores the role of uncertainty and luck, leading people to repeat lucky mistakes or abandon good strategies after unlucky results.
Q3. Why is it useful to record your probability estimates before an outcome is known?
- A. It allows you to compare your forecasts against actual results and check your calibration over time ✓
- B. It guarantees that future outcomes will match your predictions
- C. It removes the need to consider alternative scenarios
- D. It makes it easier to hide mistakes from others
Why: Recording predictions in advance creates a track record. Over many decisions, you can see whether events you call 70% likely actually occur about 70% of the time, which reveals overconfidence or underconfidence.
Q4. After receiving new evidence that contradicts your earlier decision basis, what is the most sound response?
- A. Ignore the evidence because you already committed to the original plan
- B. Update your beliefs and reconsider the decision in proportion to the strength of the evidence ✓
- C. Wait until the original plan fails completely before reacting
- D. Defend the original decision to protect your reputation
Why: Rational revision means adjusting beliefs in proportion to how strongly new evidence supports or undermines them. Clinging to sunk commitments or waiting for total failure wastes opportunities to improve.
Q5. Which practice best helps distinguish skill from luck when reviewing a series of past decisions?
- A. Reviewing only the most recent decision in detail
- B. Looking at many decisions over time and comparing the process used with the spread of outcomes ✓
- C. Focusing only on decisions that produced excellent results
- D. Assuming that any success was due to skill and any failure to luck
Why: A single outcome is noisy. Reviewing many decisions reveals patterns: consistently good processes tend to produce good results on average, while luck averages out over a large sample. Selecting only winners or assigning causes arbitrarily distorts the lesson.