Question:
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 just 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 plugs.
(a) For each spark plug, what is the probability that it will not fail?
(b) If only 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? Calculate using the appropriate formula.
(c) If two or more spark plugs fail, the plane will crash. What is the probability that this happens? You may use software to help determine this probability.
(d) Given that one spark plug fails, what is the probability that the plane will still land safely?