Level 2: Fair or unfair?

Probability · level 2 of 8 · rough age 7-8 (a guide for parents; anyone can start anywhere)

In level 1 you sorted things into sure, maybe and never, and found that more ways means more likely. In this level the maybe pile opens up into a whole chance line, and you become a judge of games: you decide whether a game is fair, and fix it when it is not. You play detective with a hidden bag, race horses with two dice, find out why a coin cannot remember, and learn to make predictions that are close without being exact.

Lesson	You will be able to
The chance line	Place events on a line from impossible to certain, and explain why one event goes further along than another
Fair games	Decide whether a game is fair by counting every way it can turn out, and fix an unfair game in more than one way
Experiments and tallies	Use many draws from a hidden bag to make a good guess about what is inside, and say how sure the guess is
The dice sum race	Find all 36 ways two dice can land, and explain why horse 7 wins the race more often than any other
Chance has no memory	Explain why the next flip after five heads is still an even chance, and when the past really does change the chances
Making predictions	Predict about how many times something will happen in many tries, and say how close the real answer is likely to be

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