Expected Value and Payback: Math Made Easy

Expected value helps us understand the average outcome of a probability scenario over many attempts.In our example, we have a game with two possible outcomes.To calculate the expected value, we multiply each outcome by its probability.For the winning outcome, we multiply one hundred dollars by zero point five.For the losing outcome, we multiply negative fifty dollars by zero point five.Adding these together gives us our expected value of twenty-five dollars.Let's see how this plays out over multiple trials.The general formula for expected value can be written as the sum of each outcome multiplied by its probability.Over many trials, the actual average tends to converge to our calculated expected value of twenty-five dollars.Payback percentage tells us how much of our investment we can expect to get back over time.Let's look at a simple example using a slot machine.If we invest one hundred dollars and expect to get back ninety-five dollars, we can calculate the payback percentage.Let's compare different investment options, each starting with a thousand dollar investment.We can calculate the payback percentage for each investment using our formula.Here's a visual representation of the payback percentages for each investment.When analyzing payback percentages, remember these important points.Now that we understand how to calculate payback percentage, let's move on to practical applications.When comparing investment options, we need to consider both expected value and payback percentage.Investment B offers both a higher expected value at twelve hundred dollars and a better payback percentage at ninety-five percent.Let's look at a practical business example. Consider a fifty thousand dollar expansion opportunity.We calculate the expected value by multiplying potential outcomes by their probabilities.Insurance decisions also benefit from expected value calculations. Let's analyze an insurance policy.Different investments come with varying levels of risk. Here's how we can visualize risk levels across different options.Let's compare different investment types and their risk-return profiles.