Topic 6 · Probability · Lesson 6.5

Expected Value Lab

Define the outcomes of a chance situation — each with a value and a probability — and watch the expected value compute live. Negative E(X) is the house edge. Try the carnival game preset and see why every gambling operation is engineered to make the player a net loser per play.

Expected value of a discrete random variable

E(X) = Σ value × probability

With the current setup, the expected value per play is −$1.67. Over 1,000 plays the average player would lose $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

Outcomes probability sum: 1.000 ✓

Label	Value ($)	Probability	Contribution

Try a scenario