Problem 307

Chip Defects

k defects are randomly distributed amongst n integrated-circuit chips produced by a factory (any number of defects may be found on a chip and each defect is independent of the other defects).

Let p(k,n) represent the probability that there is a chip with at least 3 defects.
For instance p(3,7) ≈ 0.0204081633.

Find p(20 000, 1 000 000) and give your answer rounded to 10 decimal places in the form 0.abcdefghij.

电路瑕疵

在一个工厂生产的n块集成电路上随机分布有k个瑕疵（一块集成电路上可能有任意数量的瑕疵，瑕疵之间相互独立）。

记p(k,n)为存在一块集成电路上面有至少3个瑕疵的概率。
例如，p(3,7) ≈ 0.0204081633。

求p(20 000, 1 000 000)，并将你的答案四舍五入到10位小数，即形式为0.abcdefghij。