Why do we have so few neutrinos to study? According to Wikipedia most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5^10) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.

However the IceCube Neutrino Observatory or other neutrino detectors only detect a few neutrinos every year. Why?
It's not that the neutrino detectors don't have a chance of detecting a neutrino, but that the neutrinos do not interact with matter (well hardly ever). 

If there are $6.5\times 10^{10}$ neutrinos per second per $cm^2$ and if the detector has an area of $10^{6} cm^2$, and it detects 1 neutrino per year, then 1 out of $2.05\times 10^{24}$ neutrinos interacts with the detector. $2.05\times 10^{24}$ pass through the detector unnoticed.