不確実性と期待値

Outcomes are the possible results that can occur in an uncertain situation, such as a company performing well or average. Payoffs represent the monetary value associated with each outcome. For example, a higher bonus outcome might have a payoff of $10,000, while a lower bonus outcome has a payoff of $5,000.

Expected value is calculated by multiplying each payoff by its probability of occurring, then summing all weighted payoffs. For instance, if a $10,000 payoff has a 0.5 probability and a $5,000 payoff has a 0.5 probability, the expected value equals (0.5 × $10,000) + (0.5 × $5,000) = $7,500.

Probability quantifies the likelihood that a particular outcome will occur in an uncertain situation. It ranges from 0 to 1, where higher probabilities indicate more likely outcomes. Understanding probability is essential for calculating expected value and making informed decisions when facing uncertainty.

Expected value represents the average payoff across all possible outcomes, weighted by their probabilities. This metric helps decision-makers evaluate uncertain situations by providing a single numerical estimate of what they can expect to earn on average, enabling comparison between different risky choices.

Uncertainty arises when future outcomes are unknown and influenced by chance or external factors. A college graduate might secure a high-paying job immediately or remain unemployed for an extended period. Similarly, a basketball team may win a championship game and earn prize money or lose and earn nothing, demonstrating how uncertainty shapes business and career outcomes.

Expected income is calculated by multiplying each possible income outcome by its probability and summing the results. For example, if a team has a 0.5 probability of earning $10,000 and a 0.5 probability of earning $6,000, the expected income is (0.5 × $10,000) + (0.5 × $6,000) = $8,000, providing an estimate of average earnings.

By calculating expected value, decision-makers can quantify the average outcome of uncertain situations and compare different options objectively. This analysis helps individuals and businesses evaluate risky choices systematically, moving beyond guesswork to evidence-based decisions that account for both payoffs and their probabilities.