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Gaokao maths tips: probability and statistics

The formulas are short. The reading is what trips students up.

Probability is the section of the gaokao maths paper that most rewards careful reading. The arithmetic is not hard; deciding which formula applies is, and that is almost always a reading problem rather than a maths one.

Ask two questions before anything else: is this with or without replacement, and does order matter? Those two answers tell you whether you are counting combinations, permutations or something else entirely.

For conditional probability, write P(A|B) = P(A∩B) / P(B) out in full before you substitute any numbers. Half the mistakes on this topic come from calculating P(A∩B) and reporting it as P(A|B).

Expected-value questions almost always come down to E(X) = Σ xᵢ · pᵢ. Build the distribution table first, then write the formula.

For the normal-distribution question at the end of the section, memorise the three intervals: μ±σ ≈ 68.3%, μ±2σ ≈ 95.4%, μ±3σ ≈ 99.7%. The question tests whether you can read a table, not whether you can integrate.

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