==> 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.