Let's Make a Deal! Probability Lesson!

"This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door." Is switching better or worse than staying? Is there a difference?

You decide, or let this page decide for you: http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

http://www.straightdope.com/classics/a3_189.html

Oh god, here we go again. Everyone knows that it's better to switch, yet knowing all the math behind it won't make you any more sure as to why.

0.999~ = 1

,

Numbermind said:

0.999~ = 1

oh sweet merciful christ, not this

Epyo said:

"This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door." Is switching better or worse than staying? Is there a difference?

You decide, or let this page decide for you: http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

You know this was just in a game forum I just checked About and hour or so ago. Funny how things get around

This paradox always makes my head asplode.

Psyonisis said:

All of Cecil's attempts to explain the logic are unacceptable.

Yep, it's quite simple really. If you pick the right door to start with (1/3 chance), you don't switch (as you're already on the right one). If you pick the wrong door to start with (2/3 chance) you do switch (as you're on a wrong one and the other one is revealed by the host). You've just got to decide which one you think you've done, and the chances say which is more likely.