Assume that in the composition of a book there exists a constant probability 0.0001 that an arbitrary letter will be set incorrectly. After composition, the proofs are read by a proofreader, who discovers 90% of the errors. After the proofreader, the author discovers half of the remaining errors. Find the probability that in a book with 500 000 printing symbols there remain after this no more than six unnoticed errors.