New spark plugs have just been installed in a small airplane with a four-cylinder engine. There is one spark plug per cylinder, so four spark plugs have been installed. For each spark plug, the probability that it is defective and will fail during its first 20 minutes of flight is 1/10,000, independent of the other spark plugs.
a. For each spark plug, what is the probability that it will not fail?
b. If one spark plug fails, the plane will shake and not climb higher, but it can be landed safely. What is the probability that this happens (as it did for one of the authors of this book)?
c. If two or more spark plugs fail, the plane will crash. What is the probability that this happens?