Extending the work of Deborah L. Massari and Kimberly L. Patti,
this paper makes progress toward finding the probability of
elements randomly chosen without repetition generating a finite abelian group, where
is
the minimum number of elements required to generate the group. A
proof of the formula for finding such probabilities of groups of the form
,
where
and
is prime, is given, and the result is extended to groups of the form
, where
and
is
prime. Examples demonstrating applications of these formulas are given, and aspects
of further generalization to finding the probabilities of randomly generating any finite
abelian group are investigated.
