go ahead... be a heretic 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":

• Are you posting in the right place? Check out Where do I post X? to know for sure.
• Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
• Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
• Want more info? How to link or or How to display code and escape characters are good places to start.

Create A New User
Domain Nodelet?
Chatterbox?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others lurking in the Monastery: (2)
As of 2021-12-05 08:42 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
R or B?

Results (31 votes). Check out past polls.

Notices?