Using the binomial directly is a good way to get the probability of 0 heads. Note, though, that the U.S. population is in the neighborhood of 300 million, not 3 million (as you seem to have used).
(1 - 2⋅10⁻⁶)^(3⋅10⁸) ≈ 10⁻²⁶¹
https://www.wolframalpha.com/input/?i=%281+-+2+*+10%5E-6%29%...