Just another Perl shrine PerlMonks

### Comment on

 Need Help??
The trick here – and there is a trick – is a subtle use of equivocation: You make a claim about one problem but then explain the claim in terms of another problem that is subtly yet significantly different.

In the first problem, each envelope can contain any number. In the second problem, however, you require that the distribution of numbers have a "continuous probability distribution with non-zero density everywhere." These problems are not the same.

To see why, imagine an infinite number line representing all numbers. If you pick any segment on this line, say that between 0 and 1, the portion of the line that the segment represents is zero. Hence the probability density function over the segment is also zero, which contradicts the assumption made in your analysis.

If we repeat your analysis, this time using the distribution of numbers for your originally stated problem, we find that the probability of picking a number in between your two numbers is zero, and thus knowing the first number provides no benefit. Our intuition turns out to be correct.

In reply to Re: Spooky math problem by tmoertel
in thread Spooky math problem by tilly

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":

• Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
• Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
• Read Where should I post X? if you're not absolutely sure you're posting in the right place.
• Posts may use any of the Perl Monks Approved HTML tags:
a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
• You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
 For: Use: & & < < > > [ [ ] ]
• Link using PerlMonks shortcuts! What shortcuts can I use for linking?

Create A New User
Chatterbox?
 [Corion]: marto: Great! The German Perl Workshop was a success even though things looked dire before, and I'm now back at home with two days off work still to go ;) [Corion]: I hope things have settled down a bit for you and the boys are alright?! [choroba]: Good morning, if a bit rainy [marto]: life is a struggle :P I'm glad the GPW went well.

How do I use this? | Other CB clients
Other Users?
Others examining the Monastery: (5)
As of 2017-06-29 08:04 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
How many monitors do you use while coding?

Results (655 votes). Check out past polls.