Topic 6 · Interactive tool
Expected Value Lab
List what can happen, what each outcome is worth, and how likely it is. The expected value is what you win or lose per play, on average, if you played forever.
Expected value of a discrete random variable
E(X) = Σ value × probability
On average this is worth −$1.67 per play. Over 1,000 plays, a player would expect to lose about $1,667.
Expected value E(X)
−$1.67
average per play
Probability sum
1.000
must equal 1.000
Verdict
Bad bet
player loses on average
Show the working
Multiply each outcome’s value by its probability, then add them up. Losses go in as negative values.
Outcomes probability sum: 1.000 ✓
| Label | Value ($) | Probability | Contribution | Remove |
|---|
Try a scenario