Brain teaser

[davidd]

In the marble example:

To keep the procedure the same as the donkey problem, the host would have to remove 98 black marbles, so you know the white marble is either in your hand or in the bag. You then get the option of re-chosing. At this point there are only two possibilities. Either the marble is in your hand, or in the bag. Since you can re-choose, I still say it is 50/50 at this point. The previous 98 marbles have been removed from the equation. At the beginning we knew that one in the 100 was white, now we know that one in two is white, and we get to choose one.

[Milbs1]

In the marble example:

To keep the procedure the same as the donkey problem, the host would have to remove 98 black marbles, so you know the white marble is either in your hand or in the bag. You then get the option of re-chosing. At this point there are only two possibilities. Either the marble is in your hand, or in the bag. Since you can re-choose, I still say it is 50/50 at this point. The previous 98 marbles have been removed from the equation. At the beginning we knew that one in the 100 was white, now we know that one in two is white, and we get to choose one.

Yes, but you know the one in your hand was a 1 in 100 chance to be white. Sure it could be the white one, but chances are its not....
Put it another way.... if you could choose the single marble in your hand, or the other 99 marbles, which would you choose?? Essentially swapping gives you the choice of the other 99 marbles.

[Steve Axford]

The really interesting thing about this problem is why so many of us just can't get it right. Somehow our brains are just wired wrong - for this problem at least.

[Bax]

Somebody start a poll, with this exact same scenario.

Lets see how many people get it right, then justify their reasons why they picked it

[ameerat42]

Somebody start a poll, with this exact same scenario.

Lets see how many people get it right, then justify their reasons why they picked it

What? You mean like a donkey vote?

[davidd]

OK........ suddenly I get it.... makes you think tho'

[Speedway]

It's still 50/50 no matter what you say. Overthinking is the only problem.
Keith.

[Steve Axford]

Mmmmmm. I suggest you do this 100 times and see if you get closer to 50/50 or to 33/67. Fancy a small wager?

[davidd]

The way I realised it was like this:

Using the marbles version, it's easier to see the difference.

You choose 1 marble. You have a 1% chance of being right at this point.

By revealing 98 black marbles, and offering you the choice to change, the host is effectively saying " Do you want the one marble you chose originally, or the 99 that were left?"
You then choose between the white marble being the one you originally chose (1% chance) or in the other 99 (99% chance).

Simple really...

[ving]

CLICK!

[Steve Axford]

Wonderful!!! It's a buzz when you get it, ain't it?

[ving]

Wonderful!!! It's a buzz when you get it, ain't it?

a buzz? hmm... i dont know, it still feels a bit weird.

[davidd]

Note: any posts made under my name before #107 above, were fraudulent, false, and the product of a confused brain.

I deny authorship of any of them.....

[Sezzy]

Imagine a game show.
There are 3 doors, one with a major prize and the other two with a donkey behind.
You are asked to pick a door.
You pick one.
The host then opens another door - always revealing a donkey.
The host then asks you - do you want to change your pick?
Do you?

NO...According to your teaser, there is 'A' donkey, not two...so I'll stick with my pick thanks...there's no more donkeys...

[Kafter244]

Often logic and mathematics don't go as closely together as people think! Lol. I live this problem...the other way to look at it is this...

If the host had originally said 'behind these three doors are two donkeys and a car...you can pick one door or you can pick two...' what would you do? You' take two doors obviously, because your chance of one o them bein the car is greater than if you picked one door.

When the host opens the door and gives you the chance to change your mind he's effectively giving you this option as to choose two doors would (probably) give you one donkey and one car, so the likelihood is that the car is in the other door...hence takin the swap.

Love this problem, and the thread...especially the kittens!

[Kafter244]

...not a big fan of all those typo's though! Lol. Sorry folks...goddam
iPhones