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Using probability to make fair decisions

Julie is driving her 33 children to the pool, and each of them wants to sit in the front seat. The kids hand their mom two 66-sided dice (one is red and one is yellow), and they ask her to make a fair decision about who gets to ride up front.
Match each method for choosing a child with the correct assessment of its fairness.
(Consider a system to be fair when the probabilities of each event are equal.)
Method 1\text{Method }1: Mom rolls both dice. If their total is a 22 or a 66 Abby sits up front. If their total is a 77 Bobby sits up front. If their total is an 88 or a 1212 Cam sits up front. If their total isn't 22, 66, 77, 88, or 1212 she rolls again until she gets one of those totals.
Method 2\text{Method }2: Mom rolls both dice. If they are the same number Abby sits up front. If the red die is higher, Bobby sits up front. If the yellow die is higher, Cam sits up front.
Method 3\text{Method }3: Mom rolls both dice. If both dice are 11 - 33 Bobby sits up front. If both dice are 44 - 66 Cam sits up front. If one die is 11 - 33 and the other is 44 - 66 Abby sits up front.
Decision-making method
Fairness assessment
  • Method 1\text{Method }1
  • Method 2\text{Method }2
  • Method 3\text{Method }3
  • Not fair because Abby has the least chance of getting chosen.
  • Fair
  • Not fair because Abby has the greatest chance of getting chosen.