Quiz: Flaw in answer?

[bigpooch]

Here's an interesting problem someone asked me:


QUESTION
---------

There are three independent observers around a lake and they
are located at different places on land. Each of them see a
boat sinking. It would be nice if their lines of sight
intersected at a point, but instead, they create a big
triangle in the lake. What is the probability that the boat
started sinking in the triangle? Assume that the chances
that the boat is sinking is on each side of a specific
observer's line of sight is 1/2.


In any case, I see a flaw in:


ANSWER WITH FLAW (?)
----------------------

Since the observers are independent, the probability that
the boat started sinking within the triangle is the same
as the probability it is on one side of the line of sight
for each of the three observers, which is then just (1/2) x
(1/2) x (1/2) = 1/8.


What is the major flaw in the answer, if any?

[PairTheBoard]

When you say, "on each side of a specific
observer's line of sight", he's definitely on one side or the other. How is the "correct" side determined? Doesn't it depend on what the line of sight of the other two observers is? If so, it looks like a dependence relationship with those lines of sight.

PairTheBoard