Expected Value
IntermediateExpected value is the average outcome you would expect from an uncertain situation if it could be repeated many times, calculated by multiplying each possible outcome by its probability and adding the results.
Expected value combines all possible outcomes into a single number that reflects both their size and their likelihood.
For example, consider a bet with a 50% chance of winning 110 and a 50% chance of losing 100. The expected value is 0.5 multiplied by 110, plus 0.5 multiplied by minus 100, which gives 5. On average, over many repetitions, the bet would gain 5 each time.
Expected value is used throughout finance and business. Investors use it to estimate expected returns. Insurers use it to calculate expected claims. Businesses use it to evaluate projects with uncertain outcomes, such as launching a new product that might succeed or fail.
Expected value has an important limitation: it says nothing about risk. A decision with a positive expected value can still lead to a large loss in any single case. Many people sensibly turn down bets with positive expected values if the potential loss is too large for them to bear. This is why expected value is usually considered alongside measures of risk, such as the range of outcomes or the standard deviation.
For worked examples and full lessons, visit notesbysara.org.