1. What is Expected Value?

The expected value (EV) is a fundamental concept in probability theory that represents the average outcome if an experiment is repeated many times. It's calculated by summing the products of each possible outcome with its probability of occurrence.

2. How Does the Calculator Work?

The calculator uses the expected value formula:

Where:

• \( Probability_i \) — The probability of outcome i (between 0 and 1)
• \( Outcome_i \) — The value associated with outcome i
• \( \sum \) — Summation over all possible outcomes

Explanation: For each possible outcome, multiply its value by its probability, then sum all these products to get the expected value.

3. Importance of Expected Value

Details: Expected value is crucial in decision making under uncertainty, used in fields like finance, insurance, game theory, and statistics to evaluate potential outcomes and make optimal choices.

4. Using the Calculator

Tips: Enter probabilities (must sum to 1) and their corresponding outcomes. You can add multiple outcomes using the "Add Another Outcome" button. All probabilities must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What if my probabilities don't sum to 1?
A: The calculator will still compute a result, but for proper probability theory, probabilities should sum to 1. Consider normalizing your probabilities if they don't.

Q2: Can I use percentages instead of decimals?
A: Yes, but divide by 100 first (e.g., 25% = 0.25). The calculator expects probabilities between 0 and 1.

Q3: How is expected value different from average?
A: Expected value is the theoretical average based on probabilities, while average is calculated from actual observed data.

Q4: Can expected value be negative?
A: Yes, if some outcomes are negative (e.g., in gambling or financial investments where losses are possible).

Q5: What fields use expected value calculations?
A: Finance, insurance, statistics, game theory, machine learning, and any field involving decision-making under uncertainty.