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CAIE A-Level Mathematics 5.3.2 Probability Rules

Practise choosing addition, multiplication or complement rules for simple and multi-stage events, including ordered selections, changing probabilities and several valid routes.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • multiply probabilities along each ordered route and update fractions after a no-replacement draw
  • add disjoint routes that satisfy the event, including different orders of the same outcomes
  • use one minus the unwanted event when direct enumeration would require many separate cases

5.3.2—Probability rules question 1

[Maximum number: 2]

The residents of Mahjing were asked to classify their local bus service:
- 25 % of residents classified their service as good.
- 60 % of residents classified their service as satisfactory.
- 15 % of residents classified their service as poor.

Three residents of Mahjing are selected at random.

Find the probability that one resident classified the bus service as good, one as satisfactory and one as poor.

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