Level 3: Chances as numbers

Probability · level 3 of 8 · rough age 9-10 (a guide for parents; anyone can start anywhere)

In level 2 you described chances in words: unlikely, even chance, likely. In this level chances become numbers from 0 to 1. You learn to list every possible outcome, to count the ones you want, and to turn the count into a fraction. Then you test the numbers against real experiments, and find out when the fraction rule works and when it does not.

Lesson	You will be able to
Outcomes and events	List the sample space of an experiment and write any event as a group of outcomes
Probability as a fraction	Find a probability as favourable outcomes over all outcomes, place it on the scale from 0 to 1, and compare chances
The chance of not happening	Use \(P(\text{not } A) = 1 - P(A)\), and say the opposite of an event correctly
Two dice: 36 outcomes	Use the 6-by-6 table to find the chance of any total, and explain why 7 is the most likely
Experimental and theoretical probability	Work out relative frequencies, and explain in plain words why they settle down as the number of tries grows
Equally likely or not	Tell when outcomes are equally likely, and find probabilities by splitting, measuring or experimenting when they are not

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