A naive probabilistic approach to the problem of testing all possible combinations:

Instead of testing all possible combinations, we could try to estimate the total number of bugs by a probabilistic approach. Given a list of all possible combinations, we randomly select two subsets of combinations for Tester One and Two to test.

Let T be the total unknown number of possible bugs associated with all combinations.
Let A be the number of bugs found by Tester One.
Let B be the number of bugs found by Tester Two.
Let C be the number of bugs found by both Tester One and Two.
Hence (let P(X) be probability of X)

P(A and B) = P(C)     (by definition)

  P(A)P(B) = P(C)     (independence assumption)

  A     B     C
 --- * --- = ---
  T     T     T

      A*B
     ----- = T
       C
That means, the less bugs both Tester One and Two found at the same time, the more likely there're still a large number of unknown bugs yet to be found.

Or, the more common bugs found by both Tester One and Two, the more likely that they have found most of the bugs.


_________
If someone wanna see the Venn diagram: 
   +----------------------------------+
   |                                  |
   |    +------------+                |
   |    |            |        T       |
   |    |    A       |                |
   |    |            |                |
   |    |     +------|-------+        |
   |    |     |  C   |       |        |
   |    +-----|------+       |        |
   |          |          B   |        |
   |          |              |        |
   |          +--------------+        |
   |                                  |
   +----------------------------------+

In reply to Re: Testing by Contract by chunlou
in thread Testing by Contract by Ovid

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.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, 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, summary, 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:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.