Paradoxes, puzzles, conundrums

[Desi]

In a scene from Movie 21, the professor asks a student to pretend he's on a gameshow. There are 3 doors; behind one of the doors there is a car and he asks the student to choose one of the doors. The student chooses door number 1. The professor then opens door number 3 and exposes a dud prize on the other side, not the car. He then asks the student, would you like to stay with your choice of door number 1 or would you like to change it to door number 2 and explain your choice. What would you do and why? Would you switch?

[boca]

In a scene from Movie 21, the professor asks a student to pretend he's on a gameshow. There are 3 doors; behind one of the doors there is a car and he asks the student to choose one of the doors. The student chooses door number 1. The professor then opens door number 3 and exposes a dud prize on the other side, not the car. He then asks the student, would you like to stay with your choice of door number 1 or would you like to change it to door number 2 and explain your choice. What would you do and why? Would you switch?

Did the professor know what was behind door#3 (or for that matter what is behind any of the doors)?

[fantoosh]

In a scene from Movie 21, the professor asks a student to pretend he's on a gameshow. There are 3 doors; behind one of the doors there is a car and he asks the student to choose one of the doors. The student chooses door number 1. The professor then opens door number 3 and exposes a dud prize on the other side, not the car. He then asks the student, would you like to stay with your choice of door number 1 or would you like to change it to door number 2 and explain your choice. What would you do and why? Would you switch?

IMO, there are 3 step here:
1. Initially the probability of each door having car behind it is, 1/3
3. From the student's perspective, once the door 3 is opened, doors 1 annd 2 will have probability of 1/2 each.
2. After the student has made his initial choice i.e. door 1, the professor can open only one of the remaining 2 doors i.e. either door 2 or door 3.
Also he has to be 100% sure that car is not behind the door which he wants to open i.e. door 3.

Once he decides to open door number 3 and car is not found, the probability of car being behind door 2 is 1/3+1/3= 2/3.

Hence the student should switch to door 2 though its quite possible that he may still lose.

[asdqwe2k]

it is all explained here..
http://en.wikipedia.org/wiki/Monty_Hall_problem

In a scene from Movie 21, the professor asks a student to pretend he's on a gameshow. There are 3 doors; behind one of the doors there is a car and he asks the student to choose one of the doors. The student chooses door number 1. The professor then opens door number 3 and exposes a dud prize on the other side, not the car. He then asks the student, would you like to stay with your choice of door number 1 or would you like to change it to door number 2 and explain your choice. What would you do and why? Would you switch?

[Desi]

it is all explained here..
http://en.wikipedia.org/wiki/Monty_Hall_problem

Thanks, Yes, am aware of the Monty Hall, but was eliciting member views and reasoning.

[Desi]

it is all explained here..
http://en.wikipedia.org/wiki/Monty_Hall_problem

Thanks, Yes, am aware of the Monty Hall, but was eliciting member views and member reasoning.

[Desi]

it is all explained here..
http://en.wikipedia.org/wiki/Monty_Hall_problem

asdqwe2k, Thanks, Yes, I am aware of the Monty Hall, but was eliciting member views and member reasoning.

[boca]

http://www.newscientist.com/article/dn18907-illusions-contest-six-ways-to-see-two-curves.html?DCMP=OTC-rss&nsref=online-news
[quote]A simple animation has been found to offer our brains many possible interpretations. Jan Kreml?269;ek from Charles University in Hradec Kr?v?Czech Republic, discovered six different ways of perceiving a moving sine graph drawn with dots. The curves often seem to undulate like two ribbons, but the animation can also seem to have depth, with one curve seeming to be further back than the other.
2010
The dotted arcs can also look like a spindle shape that revolves and snakes along. If you keep staring, the curves can seem to revolve vertically around a static rod, first in one direction, then the other. The animation can also look like a series of bouncing dots, but this is very hard to perceive without overlaying vertical bars on top of it. "Our brain is able to reconstruct different learned interpretations, but only one can be perceived at a time," says Kreml?269;ek. He came across the illusion by chance while preparing graphs for a lecture in signal processing.
[/quote]See it: http://www.lfhk.cuni.cz/elf/people/jan/illusion/ambient_mot.html

2010 Best Illusion Contest -> http://illusioncontest.neuralcorrelate.com/cat/top-10-finalists/2010/ (the above won the 3rd place).

[dbs]

A murderer is condemned to death.
He has to choose between three rooms.
The first is full of raging fires,
the second is full of assassins with loaded guns, and
the third is full of lions that haven't eaten in 3 years.

Which one should he choose?

[libertarian]

A murderer is condemned to death.
He has to choose between three rooms.
The first is full of raging fires,
the second is full of assassins with loaded guns, and
the third is full of lions that haven't eaten in 3 years.

Which one should he choose?

Third one. Because the lions will be dead by now.