Random selection fairness

Questions asking whether a proposed random selection method is fair, or to design a fair selection method using given random devices.

2 questions

CAIE S2 2013 June Q1
1 Marie wants to choose one student at random from Anthea, Bill and Charlie. She throws two fair coins. If both coins show tails she will choose Anthea. If both coins show heads she will choose Bill. If the coins show one of each she will choose Charlie.
  1. Explain why this is not a fair method for choosing the student.
  2. Describe how Marie could use the two coins to give a fair method for choosing the student.
CAIE S2 2019 June Q3
3 Luis has to choose one person at random from four people, \(A , B , C\) and \(D\). He throws a fair six-sided die. If the score is 1 , he will choose \(A\). If the score is 2 he will choose \(B\). If the score is 3 , he will choose \(C\). If the score is 4 or more he will choose \(D\).
  1. Explain why the choice made by this method is not random.
  2. Describe how Luis could use a single throw of the die to make a random choice.
    On another day, Luis has to choose two people at random from the same four people, \(A , B , C\) and \(D\).
  3. List the possible choices of two people and hence describe how Luis could use a single throw of the die to make this random choice.