==> probability/darts.s <== Since the three darts are thrown independently, they each have a 1/3 chance of being the best throw. As long as the third dart is not the best throw, it will be worse than the first dart. Therefore the answer is 2/3. Ranking the three darts' results from A (best) to C (worst), there are, a priori, six equiprobable outcomes. possibility # 1 2 3 4 5 6 1st throw A A B B C C 2nd throw B C A C A B 3rd throw C B C A B A The information from the first two throws shows us that the first throw will not be the worst, nor the second throw the best. Thus possibilities 3, 5 and 6 are eliminated, leaving three equiprobable cases, 1, 2 and 4. Of these, 1 and 2 have the third throw worse than the first; 4 does not. Again the answer is 2/3.