In a letter to the editor that appeared in the February 23, 1987, issue of U.S. News and World Report, a reader discussed the issue of space-shuttle safety. Each "criticality 1" item must have a 99.99% reliability, by NASA standards, which means that the probability of failure for a "criticality 1" item is only 0.0001. Mission 25, the mission in which the Challenger exploded on takeoff, had 748 "criticality 1" items. Use the Poisson approximation to the binomial distribution to determine the approximate probability that
a. None of the "criticality 1" items would fail.
b. At least one "criticality 1" item would fail.