Austen, a rocket designer, has come to Chris, a reliability expert, with the following problem:
“The vehicle is designed. We can use two large engines or four small engines and get the same thrust and the same weight. However, we know that the engines are subject to catastrophic failure, and we have designed the vehicle so that we will still get into orbit if half of the engines fail. Now, if you tell me the probability of an engine failing in the time required to get into orbit, I can decide whether to use two or four.”
Chris replied, “We have analyzed the test data on the engines and have found that the large and small engines have the same probability of failing in a given time. I can assure you that it makes no difference whether you use two or four engines. However, this failure probability is classified top secret and I cannot give it to anyone.”
Austen said, “Never mind. From what you have just told me, I can calculate by myself the failure probabilities of an engine and of the rocket.”
a. What is the failure probability for a single engine?
My answer: 0.5?
b. What is the failure probability for the rocket?
My answer 0.5?