Jailers Paradox Cousin of the Monty Hall Paradox

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Jailer’s Paradox Cousin of the Monty Hall Paradox

Jailer’s Paradox Cousin of the Monty Hall Paradox

Jailer’s Paradox • If the Monty Hall paradox did not make intuitive sense, perhaps

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

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

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

Jailer’s Paradox - Solution • Here is the solution from “Randomness”, by Deborah Bennett Scenario Prisoner’s fate Jailer says this prisoner will go free Probability of this scenario Adam Bill Carl 1 a Ω Ш Ш Bill 1/6 1 b Ω Ш Ш Carl 1/6 2 Ш Ω Ш Carl 1/3 3 Ш Ш Ω Bill 1/3

Simpson’s Paradox • If the acceptance rate of women is higher than the rate

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 Women Men Dept. Applied Accepted 1 50 20 (40%) 30 10 (33%)

Simpson’s Paradox Women Men Dept. Applied Accepted 1 50 20 (40%) 30 10 (33%) 2 40 30 (75%) 70 50 (71%) College Total 90 50 (56%) 100 60 (60%) From “Randomness”, by Deborah Bennett

Simpson’s Paradox – More Slanted Star Athletes Star Scholars Dept. Applied Accepted Sports Journalism

Simpson’s Paradox – More Slanted Star Athletes Star Scholars Dept. Applied Accepted Sports Journalism 30 15 (50%) 1 0 (0%) Rocket Science 1 1 (100%) 30 20 (67%) College Total 31 6 (52%) 31 20 (65%)

Simpson’s Paradox - Revisited Women Dept. Men Total Apply Accept Rate 1 50 20

Simpson’s Paradox - Revisited Women Dept. Men Total Apply Accept Rate 1 50 20 (40%) 30 10 (33%) 80 30 38% 2 40 70 80 73% 90 50 (71%) 60 (60%) 110 College Total 30 (75%) 50 (56%) 100 Adapted from “Randomness”, by Deborah Bennett