Yeah, it doesn't make a difference until the planes cover a significant area of the Earth, in which case just multiplying by the numbers of planes will be wrong

Yeah, it doesn't make a difference until the planes cover a significant area of the Earth, in which case just multiplying by the numbers of planes will be wrong for the same case that the initial calculation was wrong. Then it would be 1-(1-5.82e-13)^3500 in this case, too.