Level 4: Two things at once

Probability · level 4 of 8 · rough age 11-12 (a guide for parents; anyone can start anywhere)

In level 3 you found chances for one experiment at a time. In this level two or more things happen together: a coin and a die, two spinners, three flips in a row. Tables and tree diagrams show every outcome, and the multiplication rule for independent events explains why the numbers come out as they do. When a problem is too hard to work out, you simulate it; and you learn what an expected count does, and does not, promise.

Lesson	You will be able to
Compound events with tables	List the outcomes of two experiments in a table, explain why there are \(m \times n\), and read "and" and "or" events from it
Tree diagrams	Draw a tree for several stages, multiply along paths and add across them, and show that P(exactly two heads in three flips) is 3/8
Fractions, decimals and percents	Change a probability between the three forms, compare chances, and explain what "40% chance of rain" means
Independent events	Decide whether two events are independent, and use \(P(A \text{ and } B) = P(A) \times P(B)\) with a reason why it works
Simulations	Design a fair simulation with dice, coins or random digits, run it, and check it against an exact answer
Expected counts	Find an expected count \(n \times p\), describe how far real counts usually land from it, and spot a result too odd to be chance

Previous: Level 3: chances as numbers · Next: Level 5: probability rules · Probability topic page