You don't have to find a simple expression for the probability, just make a table of the probability of P(Sn) for all the possible values of n. That should suffice.
We roll a four-sided die twice. Let the outcome of the experiment be (r1; r2) where r1
and r2 are the results of the rst and the last rolls, respectively. Assume that all possible
outcomes have equal probability. Denote by Sn the event that r1 +r2 = n and by Mk the
event that max(r1; r2) = k. Find P(Sn), P(Mk) and P(Sn\Mk), for all combinations of n
I have found P(Mk) and i can see the relationship for P(Sn). It is distributed symmetrically around Sn=5, but i cant actually find a "single" mathematical expression for the probability.