  We determine the probability distribution for relative projective objects in
an exceptional sequence of type $A_n$ of any length. We show that these events
(the $j$-th object in an exceptional sequence of length $k\le n$ being
relatively projective) are independent of each other and from the length of the
sequence. This gives a probabilistic interpretation of the product formula for
the number of exceptional sequences of length $k$ and clusters or partial
clusters of size $k$ since the latter numbers are proportional to the number of
signed exceptional sequences of length $k$.
