5) Spaceship Problem. Fly-By-Night Spaceship Company produces a booster rocket that has 1000 vítal parts. If any one of these parts fail,
the booster will crash, so they design each part with a reliability of 99.9%,
meaning that the probability of an individual part working is 0.999.
a) What is the probability that all 1000 parts work, and the booster
does not crash? Surprising?
b) What is the minimum reliability needed for each part to insure
that there is a 90% probability of all 1000 parts working?