what is wrong with the prisoner's logic?
the unexpected hanging paradox
- Thread starter AbdalQadir
- Start date
what is wrong with the prisoner's logic?
abu nibras
Staff member
if there's still no knock on my door by 5 minutes past noon on <day x> can be used to absolutely rule out the hanging for the <day x> only, ruling out sunday by this logic is fine but a day like saturday can only be ruled out if the prisoner has reached <day x> and it is Friday, not before that, or that is what i think.
maybe someone can provide a mathematical explanation
maybe someone can provide a mathematical explanation
Y
y_r
Well isn't he assuming that he'll be given a 24 hour notice?AbdalQadir said:
Wadood
sunniport user
From aN post, he is killing Sunday, and decreased the week by one day, and then is applying the same logic to Saturday inplace of Sunday in the 6-day-week and continues on killing the whole week.
Only Sunday should be taken out. I agree with aN.
May be the 5 minutes past noon rule could be added as the third thing to notice.
Only Sunday should be taken out. I agree with aN.
May be the 5 minutes past noon rule could be added as the third thing to notice.
i think abu nibras got it spot on, and i thought of the same
the prisoner is only thinking along the lines of "if i DON'T get a knock by 5 minutes past noon on day [X]"
he is ignoring the possibility of "if i DO get a knock by 5 minutes past noon on day [X]"
where X can be ANY day of the week, from 1 to 7, 1 being monday and 7 being sunday
his logic is incomplete/flawed right from the start
he is proceeding in a backwards sequence working his way up from sunday back to monday for a possibility of a "no knock",
what about proceeding in a forward sequence working his way down from monday to friday for a possibility of a "yes knock"
BECAUSE
logically, he can be executed on any random day of the week - he should not think so unidirectionally!
he is thinking
"if i DON'T get a knock by 5 past noon on saturday, it means i have a 24 hrs notice for a sunday execution by default, so it's not possible my execution will be on sunday"
while the above logic is right, it is ONLY PARTIAL
what about "if i DO get a knock on noon monday" ? - its game over!
---
he can apply this logic of "if i don't get a knock by 5 past noon" ONLY for the days of saturday and friday as he is working backwards, eliminating the possibilities of a saturday or sunday execution 'coz
he can NOT apply this logic of "if i don't get a knock by 5 past noon" for thursday to eliminate the possibility of a friday execution too, 'coz logically speaking
he might have already gotten the knock and have already been executed on a day before thursday or friday or saturday... he is being unrealistic and seeing only the flowery possibility!
he has forgotten to apply the logical possibility of "if i DO get a knock" on the days of monday or tuesday or wednesday
---
he needs to list out the days of the week from the start of the week (monday) and then see the possibilities starting from the first day where he has a logical possibility of being executed!
he should THEN see the last day... in other words he should assume the worst case scenario first!
at least thats how i worked it out... i analysed the possibilities in the order of: monday, sunday, tuesday, saturday, wednesday, friday, thursday
---
MONDAY knock- possible ; no knock - possible
TUESDAY knock- possible ; no knock - possible
WEDNESDAY knock - possible ; no knock - possible
THURSDAY no knock - possible ; knock - possible
FRIDAY no knock - not possible because it would imply he will be executed on saturday or sunday, of which the possibilities are ruled out OR it can mean he is already executed before friday; knock - possible
SATURDAY no knock - not possible because it would imply he will be executed sunday OR he could have been executed before saturday too ; knock - also not possible because with sunday out, if he didn't get a knock on friday it would automatically imply a 24 hours notice, which is against the verdict
SUNDAY no knock - not possible as he has to be executed within the week and since he can't be executed sunday it implies he would be executed before sunday ; knock- also not possible because if he didn't get a knock by saturday, it implies a 24 hour notice for a sunday knock, which is not possible
the fundamental flaw was working only backwards from sunday to monday on the possibility of a "no knock" and thinking he couldn't be executed on friday
so mathematically speaking there are 5 possibilities of getting a knock on his door and only 4 possibilities of getting no knocks
mathematically speaking the probability of his execution on any given day would be 5/(5+4=9) or 55.55%
the prisoner is only thinking along the lines of "if i DON'T get a knock by 5 minutes past noon on day [X]"
he is ignoring the possibility of "if i DO get a knock by 5 minutes past noon on day [X]"
where X can be ANY day of the week, from 1 to 7, 1 being monday and 7 being sunday
his logic is incomplete/flawed right from the start
he is proceeding in a backwards sequence working his way up from sunday back to monday for a possibility of a "no knock",
what about proceeding in a forward sequence working his way down from monday to friday for a possibility of a "yes knock"
BECAUSE
logically, he can be executed on any random day of the week - he should not think so unidirectionally!
he is thinking
"if i DON'T get a knock by 5 past noon on saturday, it means i have a 24 hrs notice for a sunday execution by default, so it's not possible my execution will be on sunday"
while the above logic is right, it is ONLY PARTIAL
what about "if i DO get a knock on noon monday" ? - its game over!
---
he can apply this logic of "if i don't get a knock by 5 past noon" ONLY for the days of saturday and friday as he is working backwards, eliminating the possibilities of a saturday or sunday execution 'coz
he can NOT apply this logic of "if i don't get a knock by 5 past noon" for thursday to eliminate the possibility of a friday execution too, 'coz logically speaking
he might have already gotten the knock and have already been executed on a day before thursday or friday or saturday... he is being unrealistic and seeing only the flowery possibility!
he has forgotten to apply the logical possibility of "if i DO get a knock" on the days of monday or tuesday or wednesday
---
he needs to list out the days of the week from the start of the week (monday) and then see the possibilities starting from the first day where he has a logical possibility of being executed!
he should THEN see the last day... in other words he should assume the worst case scenario first!
at least thats how i worked it out... i analysed the possibilities in the order of: monday, sunday, tuesday, saturday, wednesday, friday, thursday
---
MONDAY knock- possible ; no knock - possible
TUESDAY knock- possible ; no knock - possible
WEDNESDAY knock - possible ; no knock - possible
THURSDAY no knock - possible ; knock - possible
FRIDAY no knock - not possible because it would imply he will be executed on saturday or sunday, of which the possibilities are ruled out OR it can mean he is already executed before friday; knock - possible
SATURDAY no knock - not possible because it would imply he will be executed sunday OR he could have been executed before saturday too ; knock - also not possible because with sunday out, if he didn't get a knock on friday it would automatically imply a 24 hours notice, which is against the verdict
SUNDAY no knock - not possible as he has to be executed within the week and since he can't be executed sunday it implies he would be executed before sunday ; knock- also not possible because if he didn't get a knock by saturday, it implies a 24 hour notice for a sunday knock, which is not possible
the fundamental flaw was working only backwards from sunday to monday on the possibility of a "no knock" and thinking he couldn't be executed on friday
so mathematically speaking there are 5 possibilities of getting a knock on his door and only 4 possibilities of getting no knocks
mathematically speaking the probability of his execution on any given day would be 5/(5+4=9) or 55.55%
Wadood
sunniport user
I really enjoyed this, was definitely tricky; jazakAllahu khair AbdalQadir. I do not think it is correct to give a probability of 55% on any one day, as that would be misleading. Conditional probability must be applied here.
Probabilities for Monday: 50/50
................for Tuesday: ...??
................for Wednesday:..??
................for Thursday:....??
................for Friday:.....?? (what is the probability of a knock on Friday, given that there was no knock in the previous four days OR that there was a knock the previous four days)
................for Saturday:...??
................for Sunday:.....??
Probabilities for Monday: 50/50
................for Tuesday: ...??
................for Wednesday:..??
................for Thursday:....??
................for Friday:.....?? (what is the probability of a knock on Friday, given that there was no knock in the previous four days OR that there was a knock the previous four days)
................for Saturday:...??
................for Sunday:.....??
