note
chunlou
A naive probabilistic approach to the problem of testing all possible combinations:<br><br>
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.<br><br>
<pre>
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 <i>both</i> Tester One and Two.
</pre>
Hence (let P(X) be probability of X)<br><br>
<pre>
P(A and B) = P(C) (by definition)<br>
P(A)P(B) = P(C) (independence assumption)
A B C
--- * --- = ---
T T T
A*B
----- = T
C
</pre>
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.<br><br>
Or, the more common bugs found by both Tester One and Two, the more likely that they have found most of the bugs.<br><br><br>
_________<br>
If someone wanna see the Venn diagram:
<pre>
+----------------------------------+
| |
| +------------+ |
| | | T |
| | A | |
| | | |
| | +------|-------+ |
| | | C | | |
| +-----|------+ | |
| | B | |
| | | |
| +--------------+ |
| |
+----------------------------------+
</pre>
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