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Introduction to Probability textbook Free etext

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Mon, 07/03/2006 - 14:16
disclamer
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Introduction to Probability textbook is free

Dartmouth is giving away the much-praised textbook, Introduction to Probability by Charles M. Grinstead and J. Laurie Snell, as free etext. The website also includes computer programs to go along with the book.

Quote:
Suppose you’re on Monty Hall’s Let’s Make a Deal! You are given the choice of three doors, behind one door is a car, the others, goats. You pick a door, say 1, Monty opens another door, say 3, which has a goat. Monty says to you “Do you want to pick door 2?” Is it to your advantage to switch your choice of doors?

Marilyn [vos Savant] gave a solution concluding that you should switch, and if you do, your probability of winning is 2/3. Several irate readers, some of whom identified themselves as having a PhD in mathematics, said that this is absurd since after Monty has ruled out one door there are only two possible doors and they should still each have the same probability 1/2 so there is no advantage to switching. Marilyn stuck to her solution and encouraged her readers to simulate the game and draw their own conclusions from this. We also encourage the reader to do this (see Exercise 11).

http://www.dartmouth.edu/%7Echance/teaching_aids/books_articles/probabil...

Reposted from boingboing.net

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Mon, 07/03/2006 - 15:33
#1
Hedge-o-Matic
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Introduction to Probability textbook Free etext

Whoa. Sweet!

Thanks for the great find!

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Mon, 07/03/2006 - 16:23
#2
bluesea
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Introduction to Probability textbook Free etext

yeah, thanks...score!

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Tue, 07/04/2006 - 02:24
#3
adagio_burner
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Re: Introduction to Probability textbook Free etext

Quote:
Suppose you’re on Monty Hall’s Let’s Make a Deal! You are given the choice of three doors, behind one door is a car, the others, goats. You pick a door, say 1, Monty opens another door, say 3, which has a goat. Monty says to you “Do you want to pick door 2?” Is it to your advantage to switch your choice of doors?

Marilyn [vos Savant] gave a solution concluding that you should switch, and if you do, your probability of winning is 2/3. Several irate readers, some of whom identified themselves as having a PhD in mathematics, said that this is absurd since after Monty has ruled out one door there are only two possible doors and they should still each have the same probability 1/2 so there is no advantage to switching. Marilyn stuck to her solution and encouraged her readers to simulate the game and draw their own conclusions from this. We also encourage the reader to do this (see Exercise 11).

Hmm, the quote does not recommend the book very well. People familiar with the problem know that most of the time the game rules are incomplete, and that's the source of all arguments.

The text above is a good example. The missing piece of information is whether Monty knew beforehand that he was picking a door with a goat. If he did, the probability indeed grows to 2/3. If he, however, always picks door #3 not knowing what's behind it (and this time he got unlucky, revealing a goat), then it's 1/2.

The same type of alternative arises when one tries to simulate the game. Do I always pick door #3 (and exclude the outcomes with a car behind it), or do I always pick a door with a goat? Depending on your answer, the result will be different.

Disclaimer: I did not read the book. Maybe that's exacvly the conclusion they arrive at... ;)

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Tue, 07/04/2006 - 06:55
#4
Epigone
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Re: Introduction to Probability textbook Free etext

adagio_burner wrote:
Hmm, the quote does not recommend the book very well. People familiar with the problem know that most of the time the game rules are incomplete, and that's the source of all arguments.

Disclaimer: I did not read the book. Maybe that's exacvly the conclusion they arrive at... ;)
Agreed: the quote does not recommend the book, any they do arrive at that conclusion. Continuing the quote:

Quote:
Other readers complained that Marilyn had not described the problem completely.
In particular, the way in which certain decisions were made during a play of the game were not specified. This aspect of the problem will be discussed in Section 4.3. We will assume that the car was put behind a door by rolling a three-sided die which made all three choices equally likely. Monty knows where the car is, and always opens a door with a goat behind it. Finally, we assume that if Monty has a choice of doors (i.e., the contestant has picked the door with the car behind it), he chooses each door with probability 1/2. Marilyn clearly expected her readers to assume that the game was played in this manner.

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Tue, 07/04/2006 - 09:48
#5
disclamer
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Introduction to Probability textbook Free etext

I didn't select the quote - I just reposted the blurb from boingboing.net.

I suspect, however, that judging a 520 page American Mathematical Society textbook by an out-of-context 2 paragraph excerpt is somewhat premature.

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Tue, 07/04/2006 - 12:34
#6
Epigone
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Introduction to Probability textbook Free etext

disclamer wrote:
I

A little bit full of yourself, aren't you? ;)

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Tue, 07/04/2006 - 12:52
#7
Nando
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Introduction to Probability textbook Free etext

Epigone wrote:
A little bit full of yourself, aren't you? ;)
Unless you know him personally, I think you're out of line. Even with the smiley. To me, your comment isn't funny and seems totally unwarranted.

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Tue, 07/04/2006 - 13:53
#8
Hedge-o-Matic
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Introduction to Probability textbook Free etext

Nando wrote:
Epigone wrote:
A little bit full of yourself, aren't you? ;)
Unless you know him personally, I think you're out of line. Even with the smiley. To me, your comment isn't funny and seems totally unwarranted.

I agree. Let's keep it civil, please. As of February, we were the last polite site on the internet, and it'd be a shame to lose our title!

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Tue, 07/04/2006 - 15:22
#9
Yogurt
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Introduction to Probability textbook Free etext

Er, before this becomes a pile-on, doesn't the quoted section of Epigone's mail there make it look like he only saw a post that contained the single word "I"? I suspect he's making a joke.

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Tue, 07/04/2006 - 16:14
#10
Hedge-o-Matic
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Introduction to Probability textbook Free etext

yogurt wrote:
Er, before this becomes a pile-on, doesn't the quoted section of Epigone's mail there make it look like he only saw a post that contained the single word "I"? I suspect he's making a joke.

I agree. As of March, we were the last self-correcting site on the internet. It'd be a shame to lose our title now!

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Wed, 07/05/2006 - 11:59
#11
Epigone
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Introduction to Probability textbook Free etext

yogurt wrote:
Er, before this becomes a pile-on, doesn't the quoted section of Epigone's mail there make it look like he only saw a post that contained the single word "I"? I suspect he's making a joke.

Sorry, maybe I should have been more explicit. Yes, I was agreeing with disclaimer that judgments shouldn't be made from short out-of-context quotations.
W. Somerset Maugham wrote:
The ability to quote is a serviceable substitute for wit.

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Wed, 07/05/2006 - 12:44
#12
OutsideLime
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Introduction to Probability textbook Free etext

Oh, I get it.

Epigone is taking a quote: "I", out of Disclamer's longer statement, then making a judgement: "full of yourself, etc..." on the "quote" that has been taken out of context and is only a fraction of the original statement.

Attempting, I guess, to exaggerate and illustrate Disclamer's point that it is incorrect to judge a longer work based on a fractional quote that is taken out of context.

You'll have to polish that one a bit for the next performance, Epigone. Something got lost in the delivery... ;-) I'm glad we were able to sort it out, though.

...Let's never fight again! *sniff*

~Josh

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Wed, 07/05/2006 - 16:02
#13
Hedge-o-Matic
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Introduction to Probability textbook Free etext

Now that's subtlety. Wouldn't want to play Diplomacy with Epigone, that's for sure.

Anyway, about the textbook, it's something everyone here should at least take a peek at. A formal introduction to something so central to us as game designers is exceptionaly useful, and for those who've studied the subject in the past, hey, it's free knowledge refreshment.

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