Transcript Jailer`s Paradox

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
Prisoner’s fate
Scenario
Jailer
says this
prisoner
will go
free
Probability
of this
scenario
Adam
Bill
Carl
1a
Ω
Ш
Ш
Bill
1/6
1b
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 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
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
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.
1
Men
Total
Apply Accept Apply Accept Apply Accept Accept
Rate
50
20
30
10
80
30
38%
(40%)
(33%)
2
40
College
Total
90
30
(75%)
50
(56%)
70
100
50
(71%)
60
(60%)
110
80
73%
Adapted from “Randomness”, by Deborah Bennett