Jailer’s Paradox Cousin of the Monty Hall Paradox

Jailer’s Paradox If the Monty Hall paradox did not make intuitive sense, perhaps we can look at it from a different perspective. This paradox is similar to Monty Hall, but perhaps more intuitive.

Jailer’s Paradox Instead of 3 doors, we have 3 prison cells. You are one of 3 prisoners, 2 of whom will be set free, and 1 will be put to death. Your are writing a letter to be delivered to your family in case you are executed, and you ask the jailer which of the other 2 prisoners could definitely take your letter. Would the jailer increase your odds of execution by telling you who to address the letter to?

Jailer’s Paradox As a prisoner, should you be more worried after the jailer tells you the name?

Jailer’s Paradox - Solution Here is the solution from “Randomness”, by Deborah Bennett Scenario Prisoner’s fate Jailer says this prisoner will go free Prob- ability of this scenario AdamBillCarl 1aΩШШ Bill1/6 1bΩШШ Carl1/6 2ШΩШ Carl1/3 3ШШΩ Bill1/3

Simpson’s Paradox If the acceptance rate of women is higher than the rate of men in every department in the college, how can the women’s rate be lower than the men’s for the college as a whole? From “Randomness”, by Deborah Bennett

Simpson’s Paradox WomenMen Dept.AppliedAcceptedAppliedAccepted (40%)3010 (33%) (75%)7050 (71%) College Total 9050 (56%)10060 (60%) From “Randomness”, by Deborah Bennett

Simpson’s Paradox – More Slanted Star AthletesStar Scholars Dept.AppliedAcceptedAppliedAccepted Sports Journalism 3015 (50%)10 (0%) Rocket Science 11 (100%)3020 (67%) College Total 316 (52%)3120 (65%)

Simpson’s Paradox - Revisited Adapted from “Randomness”, by Deborah Bennett WomenMenTotal Dept.ApplyAcceptApplyAcceptApplyAcceptAccept Rate (40%) 3010 (33%) % (75%) 7050 (71%) % College Total 9050 (56%) (60%)