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Math · 17 · Problem-Solving and Data Analysis

Probability

Notes

Key points

  • Probability = favourabletotal\tfrac{\text{favourable}}{\text{total}}, between 0 and 1.
  • Two-way table: find the given group — its total is the denominator.
  • “Given that”, “of those who”, “among” → conditional: shrink the denominator.
  • Complement: P(not A)=1−P(A)P(\text{not }A)=1-P(A).
  • Independent events: P(A and B)=P(A) P(B)P(A\text{ and }B)=P(A)\,P(B).
  • Expected count = probability × number of trials.

Formulas

ProbabilityP(A)=favourable outcomestotal outcomesP(A)=\dfrac{\text{favourable outcomes}}{\text{total outcomes}}
ComplementP(not A)=1−P(A)P(\text{not }A)=1-P(A)
Conditional (two-way table)P(A∣B)=n(A and B)n(B)P(A\mid B)=\dfrac{n(A\text{ and }B)}{n(B)}
OrP(A or B)=P(A)+P(B)−P(A and B)P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)
And (independent)P(A and B)=P(A) P(B)P(A\text{ and }B)=P(A)\,P(B)

Common traps

  • Dividing by the grand total in a conditional question.
  • Reversing the condition: P(A∣B)P(A\mid B) is not P(B∣A)P(B\mid A).
  • Double-counting the overlap in an “or” question.

SAT tip

In a two-way table, circle the row or column named after “given” or “of those” — that total is your denominator.

Test yourself

10 official SAT questions on Probability, easiest first.

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