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Logical Puzzle


rustyjaw
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Should you switch your guess?  

  1. 1. Should you switch your guess?



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Years ago in a philosophy class the professor presented the following brain teaser type puzzle to the class. I had forgotten all about it, but yesterday I came across it in a book I'm reading, so I thought I'd see what my esteemed fellow LCVGers might think of it.

 

You are on a game show, think of The Price is Right. The goal of the show is to win a car. You are presented with 3 doors, one door has a car behind it, the other two have balloons behind them. You are asked to pick a door. You choose a door, but it is not opened. Instead the host opens one of the doors you didn't choose to reveal balloons (the host knows what's behind the doors). You are now informed that you have a final chance to change your original guess. What should you do?

 

Please post your reasoning below (no Google cheating!)

 

If you are familiar with this puzzle, please do not post any hints, let those who have not seen it before answer and give their reason(s) why!

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A trick? Hmmmm.....

 

I choose to stay with my original guess. Why? Because my odds of guessing the right answer just jumped from 1/3 to 1/2! Since the other two doors are still not revealed, there is no sense in changing things. It's now 50/50 either way*.

 

* or perhaps not?

 

EDIT: Elaborated a bit, Ed while you were posting. :)

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Im thinking, Im thinking!

 

My first impression was that of Jeremy's. You dont know what's behind the doors, you just know that when the host opens one of the remaining doors, you have not won or lost. Changing your guess at this point would be just as blind as when you originally made your first choice, even though your chances are now 50%. What would the point be in changing your guess?

 

I'm trying to figure out if there is any difference in standing at the winning door (and not knowing it) on the first guess, and standing at the remaining balloon door (also not knowing it).

 

Hmm... I still havent voted yet. Maybe Im over analyzing this. :D

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I voted no. Can't wait to hear the philosophy behind this.

 

EDIT: Oh, my reasoning... I just don't see how the host opening a balloon door tells you anything about which of the other doors has a car behind it. No matter which door you pick the host can always open a balloon door and give you a chance to change your mind, so what difference does it make?

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Looks like I'm the second person to guess YES. I haven't read any posts yet, but the reasoning is the first time you have a 33% chance of guessing correctly, and guessing again yields a 50% chance of getting it right.

 

[EDIT] I just looked it up but won't comment on whether my choice is wrong or right along with my reasoning.

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The thing is,there is really no right or wrong answer. The probability & the odds of getting it right favor one answer over the other I'm sure...but you could go with those odds & still lose.

 

So I'm sticking with my original guess & staying with my first guess.In the end,you have to be true to yourself.

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First off let me say that I have not read anyone?s response to this before posting. I would say it makes no difference. You now have a 50/50 chance of being right (which you had all the time as the host would always unveil one of the balloon doors to you), therefore you should stick with your original gut feeling. Even though a gut feeling will not affect the outcome, it at least lets you feel responsible whether or not you win the car. You could also just flip a coin.

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The original gameshow was Lets Make a Deal, where they actually used to do this.

 

You have to switch.

 

When you make your first choice, you have a 1/3 chance of being right.

 

This chance does not change when Monty eliminates one of the wrong choices. Your first choice still has a 1/3 chance of being right (nothing will ever change those original odds), so at the end you should switch to your only remaining choice and you will have a 2/3 chance of winning. If this seems counter-intuitive you have to remember that Monty helped you out when eliminating one of the wrong choices.

 

The only way that you would have a 50/50 chance at the end, as some say, you would have had a 50% chance of being right at the very beginning. How can you have a 50% chance of being right when randomly choosing one from three? Not unless you have paranormal powers. :)

 

The odds from the original choice do not ever change.

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Originally posted by Beer Monkey@Oct 20 2004, 02:59 PM

You have to switch.

 

When you make your first choice, you have a 1/3 chance of being right.

 

This chance does not change when Monty eliminates one of the wrong choices. Your first choice still has a 1/3 chance of being right (nothing will ever change those original odds), so at the end you should switch to your only remaining choice and you will have a 2/3 chance of winning. If this seems counter-intuitive you have to remember that Monty helped you out when eliminating one of the wrong choices.

 

The only way that you would have a 50/50 chance at the end, as some say, you would have had a 50% chance of being right at the very beginning. How can you have a 50% chance of being right when randomly choosing one from three? Not unless you have paranormal powers. :)

 

The odds from the original choice do not ever change.

HA!

 

Did you copy and paste this answer, wise one?

 

No one said anything about "Monty". ;)

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Didn't copy and paste anything.

 

I wrote every word. You won't find those words posted anywhere online unless they were copies from me in the last 20 minutes.

 

When younger, I actually used to watch Lets Make a Deal, with Monty Hall. I'm just describing how the game worked. One of my favorite game shows ever, and a favorite of my whole family.

 

I'm 37 years old.

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Here's another scenario.

 

I shuffle a deck of 52 cards. I challenge you to draw the ace of spaces. If you do, I pay you $1000. You draw a card blindly, but do not look at it.

 

I then rifle through the deck and show you 50 cards that are not the ace of spades, and throw them in the trash. I place the single remaining card face down on the table.

 

If you want the ace of spades, do you keep your card, or take the one I left on the table?

 

Do you really think that you have a 50% chance of already holding the ace of spaces, the card that you drew blindly from a complete shuffled deck?

 

You switch cards.

 

Whether it is 52 cards or 3 curtains, the same rules apply.

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The only way that you would have a 50/50 chance at the end, as some say, you would have had a 50% chance of being right at the very beginning. How can you have a 50% chance of being right when randomly choosing one from three? Not unless you have paranormal powers. :)

 

But at the end you're chosing one from two.

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Originally posted by Beer Monkey@Oct 20 2004, 03:08 PM

Didn't copy and paste anything.

 

I wrote every word. You won't find those words posted anywhere online unless they were copies from me in the last 20 minutes.

 

When younger, I actually used to watch Lets Make a Deal, with Monty Hall. I'm just describing how the game worked. One of my favorite game shows ever, and a favorite of my whole family.

 

I'm 37 years old.

My bad. You didnt copy and paste anything.

 

My point was that your answer seemed exactly like the one I looked up here. Also the use of the words "counter-intuitive" and then staging the question with Monty as the host.

 

I also didnt notice the first sentence explaining why you staged the question with Monty from "Let's make a deal" when I originally read your post. I thought you edited your post to reflect that later.

 

Sorry for improperly calling you out on that.

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