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A coin spins before a cricket match. A ludo player waits for a six. A bag hides marbles of three colours. None of these can be called for sure. To call a result is to name it first. Yet each one can be measured.

This is Chapter 7 of your textbook. It is called The Mathematics of Maybe.

• Random — one result cannot be called. A long run of tosses can be described.
• A scale from 0 to 1 — chances lie between impossible and certain.
• Counting what happened — a chance from real trials.
• More tries, steadier — the share steadies as the tries grow in number.
• Counting what could happen — a chance from the set-up itself.
• When the two disagree — real rolls against the worked-out chance.
• Two things at once — a table of pairs.
• A tree of results — the same pairs, stage by stage.

A quick catch-up

These earlier ideas help. Open any to refresh it first.

• A fraction has a place on the number line.
• Divide by the whole. Then a share is a percentage.
• A ratio compares two amounts. The question decides which two.
• A new reading changes a running average.
• A claim can fit nine cases and fail the tenth.
• One try can fool you. Many tries show more.