CAIE A-Level Mathematics 5.3.4 Conditional Probability

CAIE A-Level Mathematics 5.3.4 Conditional Probability
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using tree diagrams and restricted sample spaces to calculate conditional probabilities in staged events.

How this is tested

  • draw a fully labelled tree and update branch probabilities after each event
  • sum joint outcomes satisfying the condition before forming the conditional fraction
  • restrict the denominator to outcomes consistent with the stated given information

Question 5

[Maximum number: 5]

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.

Question 5(a)

(a)

Draw a fully labelled tree diagram to illustrate this information, including all the probabilities.

[ 3 ]

Question 5(c)

(b)

Find the probability that a white counter is chosen from box A, given that one red marble and one blue marble are obtained.

[ 2 ]