Suppose two permutations are chosen at random from the symmetric group S, of degree n: What is the probability that they will generate all of S,? Netto, in his book published last century, conjectured that almost all pairs of elements from S, will generate either Sn or the alternating group A n; since 88 of all such pairs contain at least one odd permutation it would follow that the probability of generating S n is roughly 3 (see [3] p. 90). Apparently Netto's 76 year-old conjecture has remained open. The main theorem of this paper shows that Netto's conjecture is true in the following sense.