A riddle I can't figure out.

[huma]

Hmmm,an accordian and the bagpipes,and maybe a pipe organ?

[Barry the Sprout]

quote:

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Originally posted by SixOfSpades:
Actually, Legolas, that Game-Show question was famous probability puzzler for a while.....statistically, your chances of winning the prize are about 66% if you DON'T change from your original guess. It sounds bizarre (because it IS bizarre!), but it's really true. (Just remember that the game-show host KNEW which room held the prize, and all game shows like to keep their money, thank you.)

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Actually Six the probability is 66.66...% if you DO change. You pick A (prob 33.33...%) and the host opens either B or C (collectively prob 66.66...%) to reveal a chicken. All that does is let you know which one of B or C it would be if either were the prize. So you are still on a 33.33...% prob on A but if you change to the remainder then your prob is still 66.66...%.

Think of it this way. You are in a room with 100 men and are asked to guess which one is called Peter. You say number 17. The quiz master says:
"Could number 17 and number 53 stay in the room please"

Do you change your mind. Considering it was only a 1% chance of being right first time you are better off changing as you know the quizmaster must leave you the right answer.

[Legolas]

Well, the second one is a sword, but the other one is wrong. Ay other guesses?

And I'm certain it's a 50/50 chance.

No matter what you say, you'll end up with a prize and a chicken.
Then you are asked to pick any one of them. So, if you say yes, I'll stick with my guess, you're actually saying 'I'll take the door to the left'. If you say no, you're saying 'I'll take the door to the right'

Because you are offered your choice at the time there are one prize and one chicken remaining, you have a 50% chance of chosing the right one, and a 50% chance of picking the wrong one.

And if there actually is a 33% chance of the left one being the prize, then you have a total of a 83% chance of picking one of the two doors. But you have only two to choce from, so what do 17/100 contestants pick? There's an impossibility.


Two wind powered instruments? an electric guitar and an electric piano, provided they are driven by wind turbines?

[Barry the Sprout]

Don't really follow your logic Legolas but trust me it is a 66.66% chance if you change. By opening one of the two doors the quizmaster effectively tells you which one of those it is in, if it is in either. As it is a 66.66% chance of it being in one of those two you should change and guess with what he leaves.

Think of it this way. You first guess A and have a 33.33% chance of being right. By opening another door to reveal a chicken the quizmaster allows you to pick both of the other two at the same time, as you know which of those two it must be. So your chance of being right doubles.

By just saying it is 50/50 you are ignoring the fact that the quizmaster can't pick a door at random. He has to open one of the losing doors - which narrows down your options.

[SixOfSpades]

Huma gets the wind instrument one, with the pipe organ and the accordion! The bagpipes don't count, because they ARE blown into: The piper blows into the bag, then squeezes the bag under his arm to force the air out the chanter & the drones. The 3rd instrument is the Aeolean harp--its strings are so delicate that they can be moved by a slight breeze. The Greeks used to put them high on walls or up on trees to make ethereal music when the wind blew.

I think you're right about the doors, Barry--I must just be remembering wrong. For those that doubt, think of the solution this way: There is a 33.3% chance that the prize is behind Door 1. This probability WILL NOT CHANGE. The game-show host opens Door 2 to reveal a goat, leaving Door 3 as the only other option. Since Door 1 has a 33% chance of being the winner, the remaining 66.6% MUST lie with Door 3.

[Campino]

Can't follow the logics here
How can a chance from 1 out of 2 ever be something else than 50%??

[Lifetime]

Mathematically, it WOULD be a 50% chance of getting the door correct AFTER one door has been removed from your possible options.
But Mathematically, your chances of picking that door BEFORE one door has been eliminated is 33.33%
So your first guess would have a 1 in 3 chance of success, and your second chance a 1 in 2 chance of success
the chances of you picking the correct door from the start (thus getting both guesses correct) is 1/3
the chances of you picking the correct door and the wrong door (thus getting 1 of 2 guesses correct) is 1/3
the chances of you picking the wrong door twice is thus 1/3

From this, you can explain the crazy logic and gather that the chances of you getting the correct door on your second guess is 2/3 (66.66%)

Actually that logic is flawed. The probability is actually less than 2/3..its 1/6 (because you could either choose the CORRECT door then the WRONG door, OR the WRONG door then the CORRECT door, thus halving 1/3. 1/3 x 1/2 = 1/6)
Add 1/3 to 1/6 and u get 1/2

So the base probability stays at 50%, not at 66.66%

So it could be

[Lifetime]

quote:

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Originally posted by SixOfSpades:
Huma gets the wind instrument one, with the pipe organ and the accordion! The bagpipes don't count, because they ARE blown into: The piper blows into the bag, then squeezes the bag under his arm to force the air out the chanter & the drones. The 3rd instrument is the Aeolean harp--its strings are so delicate that they can be moved by a slight breeze. The Greeks used to put them high on walls or up on trees to make ethereal music when the wind blew.

I think you're right about the doors, Barry--I must just be remembering wrong. For those that doubt, think of the solution this way: There is a 33.3% chance that the prize is behind Door 1. This probability WILL NOT CHANGE. The game-show host opens Door 2 to reveal a goat, leaving Door 3 as the only other option. Since Door 1 has a 33% chance of being the winner, the remaining 66.6% MUST lie with Door 3.

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This is wrong because the 33.33% DOES change. Take this for example. You have 4 red balls and 6 blue balls in a sack.
If a ball is chosen at random, then removed, the probability of a red ball being chosen is 4/10. If the first ball chosen was red, then there is a 3/9 possibility that a red ball will be chosen at random from the sack. If that ball is also removed, then there is a 2/8 possibility that a red ball will be chosen from the sack.

Does anyone debate this?
Its the same with the doors. There is 1 correct door and 2 incorrect doors, which at first makes it a 1/3 possibility of finding the correct door. When 1 incorrect door is removed, then it becomes a 1/2 possibility of finding a correct door.

[Legolas]

Okay, try to look at it like this:

The doors are named x,y and z. Door x is the one with the prize, y and z are the chickens.

If you pick door x, either door y or door z will be opened
If you pick door y, door z opens
If you pick door z, door y opens

So no matter what door you choose, you end up with door x and a door with a chicken.
The chances of yu picking door x are 33%. The chances of you picking THAT door which results in the opening of a door with a chicken are 100%.

So, no matter what door you picked at first, the outcome is the same.


Now let us assume door z was the door with the chicken that was opened. It could have been door y equally well, but the result is the same. Still with me?


So you end up facing door x and door y. Door x contains a prize and door y contains a chicken.

At this stage, the host asks you if you want to switch doors. By saying either 'yes' or 'no', you can tell the host which door you want him to open.

Let's assume you chose door x at the beginning. If you say yes, door y opens. If you say no, door x opens.
If you chose door y, you can say yes to open door x, and no to open door y.

So, you are given a chance to pick any door you like.
One door contains a prize, one door contains a chicken.
The chances of one of the doors containing the prize is 50% right now, if you were placed in this position right away.

And, you ARE put in this position. You get to choose between door x and door y.

The 33% chance would only apply if the host asked you to pick a door, then proceed to open all three, or only the one you picked. As soon as the host gives you an oppertunity to change your mind, you get to choose all over again. Now if the situation is still the same, the chances are still the same. But if it has changed, so do the chances.

What it comes down to in the riddle is simply this:
You get to choose at a time when there are only two doors to choose from.

Hope this clears it out a bit

[Campino]

Well done Legolas [img]graemlins/thumbsup.gif[/img]

That should clear things up once and for all.