card trick

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Originally Posted by pawnhead

@Ashore. Bingo.
Multiplying anything by 0 is undefined. It's the same as saying 2 X 0 = 1 X 0, although it's true, you can't just take away the 0sYour chances are doubled to 2/3 if you change doors.



(1)Think of a number between 1 and 10.
(2)Multiply this number by 9.
(3)Add the two digits together.
(4)Subtract 5 from your answer.
(5)Associate your number with a letter from the alphabet. For example, A = 1, B= = 2, and so on.
(6)Think of a country in Europe beginning with that letter.
(7)Think of an animal where the first letter of the animals name is the last letter of the country's name. For example, England ends with "d", so you can associate that with "dog".
(8)Think of a color where the first letter of the color's name is the last letter of the animals name.

Answer (highlight) Sorry. There's no orange kangaroos in Denmark.

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any number multiplied by 9 the digits always add up to 9
subtract 5 europian country starting with D , only one Denmark
Animal starting with K most will say Kangreoo a few koala
O only colour is orange :q

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Originally Posted by Alastair

Hi John

Sorry but logic doesn't wash. With removal of 1 door, its contribution to the possibilities become redundant, and the problem reverts to the probability of finding 1 behind 2, ie 50%.

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It's already contributed to the problem so it's not redundant.

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Originally Posted by Alastair

In the absence of a distorting factor, as in the host knowing and trying to direct attention, there is an equal possibility that it is behind either door.

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Certainly the absence of the host would make the whole problem redundant.

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Originally Posted by Alastair

I would be interested to hear your justification for the 2/3 possibility, rather than the bald statement.

regards

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I'm just giving more people the opportunity to have a think about it first. :wink:

Here's one that a teacher gave us back in my school days:

Punctuate this sentence:

"James while John had had had had had had had had had had had a better effect on the teacher."

Then try this one:

"that that is is that that is not is not is that it it is"

:think:

Quote:

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Originally Posted by pawnhead

IIt's counterintuitive, but you're actually twice as likely to win if you change doors. If you change, then your winning odds are 66 2/3 %. If you don't then you've still only got a 33 1/3 % chance.

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Ok, javali's link explains it quite well.

Quote:

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Originally Posted by Alastair

Sorry but logic doesn't wash. With removal of 1 door, its contribution to the possibilities become redundant, and the problem reverts to the probability of finding 1 behind 2, ie 50%.

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This is only true when the removal of the door is independent of your choice. As the removal depends on your choice the removal is not redundant.

To get some intuition into the problem, try changing the problem a bit - there are 1000 doors. You pick one, the host opens 998, showing 998 goats behind them. Is it to your advantage to switch?

For the math:
Once you chose the door there are two possible outcomes. ither you chose the door with the car, or not. The probability of the first is 1/3, and of the second is 2/3.

If you picked a door with a goat, the host has no choice of door - he picks the one door with a goat, leaving the door with the car closed.

If you picked the door with the car, regardless of which door the host opens, the other clossed door will have a goat.

Hence in 2/3 of the cases, the other door has a car, and in 1/3 it has a goat.

Edit: For more information check http://en.wikipedia.org/wiki/Monty_Hall_problem

Goddit

In fact the chance of picking the car are still equal, what is not equal is that there were 2 chances to pick the oroginal goat, and thus get the double chance.