Maths / Probability Puzzle

Region3

Region3

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Heard this ages ago (I believe based on a real TV quiz show), but the Maths thread on here just reminded me of it.


In the final of a quiz show there are 3 doors. Behind 1 door is the star prize and behind the other 2 are booby prizes.

You are asked to pick a door as yours. The host then reveals a booby prize behind one of the 2 remaining doors, then asks you if you want to swap your door for the other remaining unopened one.

Should you swap, or stick, and why?
 
Region3 said:
Heard this ages ago (I believe based on a real TV quiz show), but the Maths thread on here just reminded me of it.


In the final of a quiz show there are 3 doors. Behind 1 door is the star prize and behind the other 2 are booby prizes.

You are asked to pick a door as yours. The host then reveals a booby prize behind one of the 2 remaining doors, then asks you if you want to swap your door for the other remaining unopened one.

Should you swap, or stick, and why?
Click to expand...

Michael Miles... Take your pick.... iirc
 
I would say swap. When you picked your door you had a 33% chance of it being right. You now have a 50% chance of the other door being the right one.

Will be happy to admit if I'm wrong on this one as it's really just a guess on my part. Or does it not actually matter whether you swap or not as each door now has a 50% chance of being correct?
 
You should always switch. It gives you a 2/3 chance of winning, when previously you had a 1/3 (and therefore have 1/3 chance when sticking). Same principle applies for shows such as Deal or No Deal - mathematically you should always switch.
 
ColchesterFC said:
I would say swap. When you picked your door you had a 33% chance of it being right. You now have a 50% chance of the other door being the right one.

Will be happy to admit if I'm wrong on this one as it's really just a guess on my part. Or does it not actually matter whether you swap or not as each door now has a 50% chance of being correct?
Click to expand...

2 ways of looking at it, and if I remember right there was disagreement between 2 branches of mathematics at the time.

On the one hand you could say 2 doors, 1 star prize = 50% chance of winning.

The way I look at it (as HowlingGale and TheDiablo above) is that if your gameplan is to swap no matter what then you win the star prize if you initially pick a booby prize (2/3) and win a booby prize if you initially pick the star prize (1/3).
 
TheDiablo said:
You should always switch. It gives you a 2/3 chance of winning, when previously you had a 1/3 (and therefore have 1/3 chance when sticking). Same principle applies for shows such as Deal or No Deal - mathematically you should always switch.
Click to expand...

Seriously!?

There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

That is so obvious I can't believe anyone can think otherwise.
 
Maninblack4612 said:
Seriously!?

There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

That is so obvious I can't believe anyone can think otherwise.
Click to expand...

When you made your choice you had a 33% chance of being right.
 
Maninblack4612 said:
Seriously!?

There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

That is so obvious I can't believe anyone can think otherwise.
Click to expand...

Before 1 door is eliminated there is a 33% chance you have picked the right door. How does removing one door improve your chances by 17%?

Or thinking about it another way; Steadfastly refusing to swap doors gives the same end result as just opening your door as soon as you pick it without removing one of the booby prizes.
 
Maninblack4612 said:
Seriously!?

There's a 50% chance you have made the right choice. Makes no difference if you swop, you still have a 50:50 chance of being right.

That is so obvious I can't believe anyone can think otherwise.
Click to expand...

You sure?

[video=youtube;7u6kFlWZOWg]https://www.youtube.com/watch?v=7u6kFlWZOWg[/video]
 
Or this one is quicker

[video=youtube;C4vRTzsv4os]https://www.youtube.com/watch?annotation_id=annotation_3308608473&feature= iv&src_vid=7u6kFlWZOWg&v=C4vRTzsv4os[/video]
 
It's 50/50 either way surely.

You had 33% at the start when choosing 1/3.

You now have to boxes and have to choose 1. Keep or switch you're still picking 1/2 or 50%.

Would like them to do the test 100 times to show of one really does have a significant edge.
 
Papas1982 said:
It's 50/50 either way surely.

You had 33% at the start when choosing 1/3.

You now have to boxes and have to choose 1. Keep or switch you're still picking 1/2 or 50%.

Would like them to do the test 100 times to show of one really does have a significant edge.
Click to expand...

They did it about 20 odd times here. If you did more then there would be no difference from a theoretical statistical viewpoint.

http://www.bbc.co.uk/news/magazine-24045598
 
Maybe I am missing something but he says that one of the doors has a booby prize behind it - it doesn't mean that both don't

So both the other two doors you haven't chosen could have a booby prize
 
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