ABSTRACT: In 1917 Hardy and Ramanujan made the fundamental observation that almost all integers n have about log(log n) prime factors. Subsequently, utilising both the Central Limit Theorem and Brun's sieve, Paul Erdos and Mark Kac proved a far reaching extension of of the Hardy-Ramanujan theorem. Thus Probabilistic Number Theory was born, and it continues to be an active area of research today. In this talk I will show that by means of a mutiplicative generalisation of the sieve, the distribution of additive functions in subsets of the positive integers can be understood. In our approach there is no dependence on the Central Limit Theorem. Also, we use the bilateral Laplace transform (moment generating function) instead of the Fourier transform (characteristic function) that was traditionally used. The talk will be accessible to non-experts.