CAIE S1 2010 November — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
TopicProbability Definitions
TypeSequential events and tree diagrams

5 Three friends, Rick, Brenda and Ali, go to a football match but forget to say which entrance to the ground they will meet at. There are four entrances, \(A , B , C\) and \(D\). Each friend chooses an entrance independently.
  • The probability that Rick chooses entrance \(A\) is \(\frac { 1 } { 3 }\). The probabilities that he chooses entrances \(B , C\) or \(D\) are all equal.
  • Brenda is equally likely to choose any of the four entrances.
  • The probability that Ali chooses entrance \(C\) is \(\frac { 2 } { 7 }\) and the probability that he chooses entrance \(D\) is \(\frac { 3 } { 5 }\). The probabilities that he chooses the other two entrances are equal.
    1. Find the probability that at least 2 friends will choose entrance \(B\).
    2. Find the probability that the three friends will all choose the same entrance.