loosely defined, a sieve is a mathematical technique for finding the rate of growth of a set of objects with a quantifiable (and hopefully small) error term. sieve techniques have wide applications in number theory and combinatorics. we will first present the idea behind sieving and present a toy example of calculating the probability that an integer is squarefree. then we will discuss poonen’s recently developed algebro-geometric sieve, which allows one to compute the probability that a hypersurface intersects smoothly with a given projective variety x over a finite field.