CAIE A-Level Mathematics 5.3.3 Exclusive and Independent Events

CAIE A-Level Mathematics 5.3.3 Exclusive and Independent Events
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise distinguishing mutually exclusive from independent events and justifying independence numerically using intersections, marginal probabilities or conditional probabilities.

How this is tested

  • calculate P(A), P(B) and P(A ∩ B) from the table, tree or equally likely outcomes
  • declare independence only when P(A ∩ B) equals P(A)P(B), showing the numerical comparison
  • distinguish disjoint events with zero intersection from independent events with unchanged probability

Question 1(c)

[Maximum number: 1]

At a college, the students choose exactly one of tennis, hockey or netball to play. The table shows the numbers of students in Year 1 and Year 2 at the college playing each of these sports.

Table for Question 1(c) — CAIE A-Level Mathematics

One student is chosen at random from the 120 students. Events X and N are defined as follows:
X: the student is in Year 1
N: the student plays netball.

Determine whether or not X and N are independent events.