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Chip Defects

Problem 307

Published on Sunday, 24th October 2010, 10:00 am; Solved by 979; Difficulty rating: 35%

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