In this case, the "very small second-order terms" add up to a whole lot of error, as the probability you came up with (22.5%) is almost 44% higher than the actual probability (15.6%).

OK, it was bogus of me to quote the result to 3 significant figures. But I still reckon +/- 44% counts as "very small second-order terms" when the object is to refute a calculation that suggests the outcome happens one time in 126,000,000...

Peter