CAIE S1 2023 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionJune
TopicIndependent Events
TypeBoth independence and mutual exclusivity

5 Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events \(A\) and \(B\) are defined as follows.
\(A\) : The sum of the two numbers is less than 6 .
\(B : \quad\) The difference between the two numbers is at most 2 .
  1. Determine whether or not the events \(A\) and \(B\) are independent.
  2. Find \(\mathrm { P } \left( B \mid A ^ { \prime } \right)\).