CAIE A-Level Mathematics 5.3.2 Probability Rules

CAIE A-Level Mathematics 5.3.2 Probability Rules
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • 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

Question 5(b)

[Maximum number: 3]

Chen has three boxes. Box A contains 5 counters, of which 3 are white and 2 are yellow. Box W contains 4 red marbles and 3 blue marbles. Box Y contains 5 red marbles and 3 blue marbles.

Chen chooses one counter at random from box A. If the counter is white, he chooses two marbles from box W, at random and without replacement. If the counter is yellow, he chooses two marbles from box Y, at random and without replacement.

Find the probability that one red marble and one blue marble are obtained.