Using probability to make fair decisions

Problem

A magician performing at a birthday party stands inside a circle of 15 kids. He’s going to choose a volunteer, and he wants each kid to have the same chance of getting chosen.
Match each method for choosing a volunteer with the correct assessment of its fairness.
(Consider a system to be fair when the probabilities of each event are equal.)
M, e, t, h, o, d, space, 1: The magician starts with the birthday boy and moves clockwise, passing out 100 pieces of paper numbered 1 through 100. He cycles around the circle until all the pieces are distributed. He then uses a random number generator to pick an integer 1 through 100, and chooses the volunteer with that number.
M, e, t, h, o, d, space, 2: The magician starts with the birthday boy and moves counter-clockwise, passing out 75 pieces of paper numbered 1 through 75. He cycles around the circle until all the pieces are distributed. He then uses a random number generator to pick an integer 1 through 75, and chooses the volunteer with that number.
M, e, t, h, o, d, space, 3: The magician starts with the birthday boy and moves clockwise, passing out 30 pieces of paper numbered 1 through 30. He cycles around the circle until all the pieces are distributed. He gives #1 to the birthday boy, #2 to the next kid, and so on. He then counts the number of windows in the room and chooses the volunteer with that number.
Decision-making method
Fairness assessment
  • M, e, t, h, o, d, space, 1
  • M, e, t, h, o, d, space, 2
  • M, e, t, h, o, d, space, 3
  • Not fair. Neither step is random.
  • Fair
  • Not fair. The papers cannot be evenly distributed.
Do 4 problems