A neutrino must pass within about 10^-18m of a quark to have any chance of interacting with it. Thus, the maximum target area that a quark presents to a neutrino is about 10^-36m^2. However, a neutrino moves so quickly and the weak interaction is so weak that experimentally only about 1 in 10^12 typical neutrinos passing a quark within this radius actually interacts significantly with it. Use this information and the fact that Avagadro's number of protons and/or neutrons has a mass of about 1g and the fact that the density of lead is about 11g/cm^3 to estimate the average distance (in light years) that a neutrino would travel through the lead before it interacts.