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WAMath MethodsSyllabus dot point

How do we calculate exact and cumulative binomial probabilities, including at-least and at-most events?

Recognise binomial conditions and calculate exact and cumulative binomial probabilities, using complements for at-least and at-most events

WACE Year 12 Mathematics Methods Unit 3 binomial probabilities: recognising the four conditions, computing exact probabilities, cumulative at-least and at-most events using the complement, with worked SCSA-style examples.

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  1. What this dot point is asking
  2. Recognising the binomial conditions
  3. Exact probabilities
  4. Cumulative probabilities
  5. At-most and between events

What this dot point is asking

SCSA Unit 3 asks you to recognise when the binomial model applies and to compute both exact and cumulative probabilities. This dot point appears in both sections; cumulative calculations are usually done with the calculator in Section Two but the reasoning is examined throughout.

Recognising the binomial conditions

Before using the formula, confirm the four conditions are met.

If any condition fails, for example sampling without replacement from a small population (which breaks independence), the binomial model does not apply.

Exact probabilities

Cumulative probabilities

At-least and at-most questions sum several exact terms. The complement is the efficient route, especially for at-least-one events.

At-most and between events

For at-most events, P(X≤k)P(X\le k) sums terms from 00 to kk. For a range, P(a≤X≤b)P(a\le X\le b) sums from aa to bb, or use P(X≤b)−P(X≤a−1)P(X\le b)-P(X\le a-1) with the cumulative function. Reading the inequality precisely is essential: P(X≥2)P(X\ge 2) excludes X≤1X\le 1, so P(X≥2)=1−P(X≤1)P(X\ge 2)=1-P(X\le 1).