Probability feels different when it starts as a game.
Instead of beginning with formulas, give students a rule: roll a die. If it lands on 6, you win 5 points. Otherwise you lose 1 point. Should you play?
Expected Value
Expected value is the long-run average result if a game is repeated many times.
For the die game, the expected value is:
- win 5 points with probability 1/6,
- lose 1 point with probability 5/6.
So the average gain is 5/6 - 5/6 = 0. The game is fair.
Why This Works for COSMO
Students can simulate first, argue second, and calculate third. The formula arrives after the intuition.
Discussion Question
How would the game change if winning gave 4 points instead of 5?