Shouldn't the expression be more like P(probes) = 1 - P(no probes) = 1 - (1 - (P(civ launches one probe)*P(probe reaches Earth)))**Nciv You can

Shouldn't the expression be more like P(probes) = 1 - P(no probes) = 1 - (1 - (P(civ launches one probe)*P(probe reaches Earth)))**Nciv You can then simply argue that P(probe reaches Earth) is small, because you don't believe that Bracewell-von Neumann probes are effective.