📈Intro to Probability for Business Unit 16 – Decision Analysis & Risk Management

Key Concepts and Definitions

• Decision analysis involves structured approaches to making complex decisions under uncertainty
• Risk management focuses on identifying, assessing, and prioritizing risks to minimize their impact
• Probability quantifies the likelihood of an event occurring, expressed as a value between 0 and 1
  • 0 indicates an impossible event, while 1 represents a certain event
• Expected value calculates the average outcome of a decision by multiplying each possible outcome by its probability
• Utility measures the subjective value or satisfaction an individual derives from a particular outcome
• Sensitivity analysis examines how changes in input variables affect the output or decision
• Scenario planning explores alternative future scenarios to make more robust decisions

Probability Basics for Decision Making

• Probability is a fundamental concept in decision making under uncertainty
• The sum of probabilities for all possible outcomes must equal 1
• Joint probability is the likelihood of two or more events occurring simultaneously, calculated by multiplying individual probabilities
• Conditional probability measures the probability of an event given that another event has occurred
  • Denoted as P(A|B), read as "the probability of A given B"
• Bayes' Theorem updates the probability of an event based on new information or evidence
• Independence means the occurrence of one event does not affect the probability of another event
• Mutually exclusive events cannot occur at the same time (rolling a 1 and a 6 on a die)

Decision Trees and Expected Value

• Decision trees visually represent the structure of a decision problem, including decision nodes, chance nodes, and outcomes
• Decision nodes (squares) represent points where the decision-maker must choose an action
• Chance nodes (circles) represent uncertain events with associated probabilities
• Outcomes (triangles) represent the final consequences of a sequence of decisions and events
• Expected value is calculated at each chance node by multiplying the probability of each outcome by its value and summing the results
• The optimal decision is the one with the highest expected value at the decision node
• Rollback analysis starts at the end of the tree and works backward to determine the optimal decision at each node

Risk Assessment Techniques

• Risk identification involves recognizing and documenting potential risks (SWOT analysis, brainstorming)
• Risk analysis evaluates the likelihood and impact of identified risks
  • Qualitative analysis uses descriptive scales (low, medium, high) to prioritize risks
  • Quantitative analysis assigns numerical values to likelihood and impact
• Probability-impact matrix plots risks on a grid based on their likelihood and potential impact
• Monte Carlo simulation generates random variables to model risk and uncertainty in complex systems
• Decision makers can develop risk mitigation strategies to reduce the likelihood or impact of risks
• Risk monitoring involves continuously tracking and reviewing risks throughout a project or decision process

Utility Theory and Risk Preferences

• Utility theory captures an individual's preferences and attitudes towards risk
• Risk-averse individuals prefer certainty and avoid risk (prefer a guaranteed $50 over a 50$100)
• Risk-neutral individuals make decisions based solely on expected value, ignoring risk
• Risk-seeking individuals prefer risk and uncertainty (prefer a 50% chance of winning $100 over a guaranteed$50)
• Utility functions map outcomes to utility values, reflecting an individual's risk preferences
• Certainty equivalent is the guaranteed amount an individual would accept instead of a risky outcome
• Risk premium is the difference between the expected value of a risky outcome and its certainty equivalent

Sensitivity Analysis and Scenario Planning

• Sensitivity analysis determines how sensitive the optimal decision is to changes in input variables
• One-way sensitivity analysis varies one input variable at a time while holding others constant
• Two-way sensitivity analysis varies two input variables simultaneously
• Tornado diagrams visually represent the sensitivity of the output to each input variable
• Scenario planning considers alternative future scenarios to make more robust decisions
  • Best-case, worst-case, and most-likely scenarios are often analyzed
• Contingency planning develops actions to take in response to different scenarios

Real-World Applications in Business

• Investment decisions, such as capital budgeting and portfolio management
• Project management, including risk assessment and mitigation planning
• Supply chain management, considering risks like supplier disruptions and demand fluctuations
• Insurance pricing and underwriting, using probability to assess risk and set premiums
• Marketing decisions, such as pricing strategies and product launch planning
• Human resource management, including succession planning and talent risk assessment

Common Pitfalls and Best Practices

• Overconfidence bias leads decision makers to underestimate risks and overestimate their ability to control outcomes
• Anchoring bias occurs when individuals rely too heavily on the first piece of information they receive
• Sunk cost fallacy is the tendency to continue investing in a decision because of past investments, even when it is no longer rational
• Framing effects occur when the way a problem is presented influences the decision
• Best practices include clearly defining the decision problem and objectives
• Involving stakeholders and subject matter experts can provide diverse perspectives and insights
• Conducting sensitivity analysis and scenario planning can help identify potential risks and opportunities
• Documenting the decision process and rationale can facilitate learning and improvement