How it works

The Expected Value Calculator helps you find the average outcome of a random event, considering all possible results and their probabilities. It's a key concept in probability and statistics for making informed decisions.

The Formula

E(X) = Σ [xᵢ * P(xᵢ)]
Where:
E(X) is the expected value
xᵢ is the value of each outcome
P(xᵢ) is the probability of each outcome

Worked Example

1. Example: Coin Flip Game

   Imagine a game where you flip a coin. If it's heads, you win $10. If it's tails, you lose $5. The probability of heads is 0.5, and tails is 0.5. To find the expected value: Outcome 1 (Heads): $10, Probability: 0.5 Outcome 2 (Tails): -$5, Probability: 0.5 E(X) = (10 * 0.5) + (-5 * 0.5) = 5 - 2.5 = $2.50 This means, on average, you can expect to win $2.50 per game.

Tips, Assumptions & Limitations

• Ensure all probabilities are entered as decimals (e.g., 25% as 0.25).
• The sum of all probabilities should ideally be 1 (or very close to it).
• Negative outcomes (losses) should be entered with a minus sign.