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> 270259 270259