Assignment:
A collection of 30 Christmas tree lights are arranged in a pure series circuit; that is, if one of the lights burns out, then the entire string goes out. Suppose that each light fails completely at random at a rate of one failure every year. What is the probability that the lights will burn from the beginning of Christmas Eve (December 24) to the end of New Year’s Day (January 1) without failure?
Provide complete and step by step solution for the question and show calculations and use formulas.