Difficult# Binomial Probability Computation (Hard)

STATS-B41AKF

Suppose a production plant has $20$ machines in operation. In any given day the probability that a machine breaks down is $.02$. If more than 2 machines break down in a day the plant will be unable to meet the day's production quota.

What is the probability that the plant will miss its production quota in more than 2 days in a non-leap year?