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**-S@m-****Member**- Registered: 2005-11-22
- Posts: 3

OK.. after seeing the results, I was wrong too...

Try this one though (taken from http://www.jimloy.com/puzz/monty.htm):

Martin Gardner's version, published in October 1959, involved three condemned prisoners, one of whom will be pardoned at random. One prisoner cons the warden into naming one of the other prisoners (other than the prisoner who is asking this of the warden) who will not be pardoned. Do this prisoner's (the one talking to the warden) chances of being pardoned then go up to 50%? This is identical to the Monty Hall trap, and this prisoner's chances are still 1/3, but the probability that the third prisoner will be pardoned have gone up to 2/3.

Thoughts?

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Thats confusing! x_x

A logarithm is just a misspelled algorithm.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

martian wrote:

thanks, and thanks putting up with my ignorance...lol ahaha

Not ignorance: you put an idea forward ... it was discussed ... you reprogrammed ... in the light of new information you changed your mind. This is the opposite of ignorance in my book.

And I liked mikau's "interplanetary" reference!

-S@m- wrote:

This is identical to the Monty Hall trap, and this prisoner's chances are still 1/3, but the probability that the third prisoner will be pardoned have gone up to 2/3.

But is it identical? Isn't the decision yet to be made? This really plays havoc with my ideas of cause and effect!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

If the decision has been made then it is identical to Monty Hall.

If the decision hasn't been made then the warden can't tell the prisoner which one can't be pardoned.

Why did the vector cross the road?

It wanted to be normal.

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**martian****Member**- Registered: 2005-11-21
- Posts: 14

Ya it is.... I finally get this yay. By one of the prisoners saying "name one of the other prisoner" or "eleiminate one of the other prisoners" is the same thing as saying "dont eliminate me" which is the same thing as saying in the first problem "I think its door blah".

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Look. Just listen at the freaking doors. Whichever makes a sound like a goat, is the one with the car behind it.

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

That's true of course ... and there may even be a different smell (depending on the type of car).

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**paharts****Member**- Registered: 2005-12-23
- Posts: 2

Can I apply this idea to the new show "Deal or No Deal"?

They start with 26 cases with varying amounts of money inside (from $.01 to $1mil). The player chooses one [lets say #4] to hold. Then randomly opens all cases except the one they chose and another [let's say 23]. There are two dollar amounts left on the board [let's say $200 and $50,000]. At the beginning of the show, there was a 1/26 chance the player chose the case with $50k.

Here's the question: does the player still have a 1/26 chance that they hold $50k? or do they have a 50% chance that they hold $50k? or do they have a 25/26 chance that they hold $50k?

And if the host offers to trade cases with the person, should they give up #4 and take #23 with a better chance that #23 has $50k?

My spouse thinks the answer is a 50% chance that one of the two remaining cases holds $50k, regardless of what went on before. Before searching for this Numb3rs episode, I thought she should trade for a better chance of getting $50k (like the car and goat scenario).

But now I'm not sure -- the player is the only person to choose cases to open so there will not be any cases opened on purpose Does that change how the calculation works?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Now, that is a very good question!

Hmmm ... if the cases have all been revealed randomly (no inside knowledge from the host), then I think the odds are equal, ie 50% chance of $50k and 50% of $200, and swapping would not improve the chances.

Or maybe not ...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I agree with MathsIsFun. The boxes were chosen randomly by the player (well, maybe not randomly, but they had no knowledge of what was inside them so it amounts to the same thing) and so there was no guarantee that the 50k would stay. The fact that it did stay implies a greater probability than before.

This contrasts with Monty Hall because the car was guaranteed to stay, so the elimination of a goat proves nothing.

Incidentally, does anyone else watch 'Deal or no Deal?' What do you think the best strategy is?

*Last edited by mathsyperson (2005-12-23 22:27:11)*

Why did the vector cross the road?

It wanted to be normal.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I find the description of the rules unclear.

The player chooses one [lets say #4] to hold. Then randomly opens all cases except the one they chose and another [let's say 23].

He "randomly" opens all the remaining cases? Why not just open all the remaining cases at once? I'm not following.

Maybe I should just stop asking questions and watch the show.

*Last edited by mikau (2005-12-24 19:08:10)*

A logarithm is just a misspelled algorithm.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Watching the show would help a great deal [or no deal ]. It's not as simple as just opening them all at once, because every so often, an evil banker tries to buy your box off you, giving an offer that depends on how much money is likely to be in your box. But, the only clues he gets to that is the amounts of money that were in the other boxes.

If you're in the UK, it's on Channel 4. Just look in a TV guide. If not, I can't help you.

Merry Christmas, everyone!

Edit: Judging by your reference to 'soccer' in another topic, I'd guess you're not. Oh well.

*Last edited by mathsyperson (2005-12-25 03:46:01)*

Why did the vector cross the road?

It wanted to be normal.

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**paharts****Member**- Registered: 2005-12-23
- Posts: 2

Thank you for your replies. I guess I will have to tell my husband he was right -- actually, I think I will say nothing and just him forget the conversation

In the U.S., it premiered last week (the week before Christmas) and was on every night at 8pm on NBC. Howie Mandel is the host. I don't know which day/timeslot they plan on putting it when the new episodes start back up. You can go to www.nbc.com/dond/game to try your hand at the online 'practice' version.

To answer 'mathsyperson', I would have sold the case for what the banker offered. But then, I would have sold the case before I got down to 2 cases I'm not much of a risk taker.

If I recall correctly, the player did not trade the cases and took the $26k the banker offered. It turned out she had the lower amount in the case she chose at the beginning of the show.

*Last edited by paharts (2005-12-27 03:43:36)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I was looking for a place to play that game a while ago and I couldn't find one, so thanks for that.

It looks like the Americans have done what they normally do to British game shows and scaled up all the prizes.

Why did the vector cross the road?

It wanted to be normal.

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**losttvseries****Member**- Registered: 2009-02-11
- Posts: 1

Numb3rs is unlike any other crime drama like CSI or NCIS or law and order. This show is a great new idea because it is unique. It uses maths to help solve crime so there is always something to back up the evidence with. It uses a lot of complex Maths equations and skills which i have picked up whilst watching the show for the last 3 1/2 years. It also has a nice mix of action (car chases and plenty of it's shooting scenes) The storylines remain exciting and imformative 85% of the time. The show is exciting and educational (in some ways) so that;s why it's my personal favourite!

When Numb3rs first came out, I was very excited. I enjoyed the idea of someone using mathematics to solve crimes and this show was much more interesting than many other shows that came off of the CSI buzz. The premise was slightly more divergent than the rest, and I enjoyed that.

WWW.DVDCOLECTS.COM

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