New spark plugs have just been installed in a small airplane with a four-cylinder engine. 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 any given spark plug, what is the probability that it will not fail during the first 20 minutes of flight?
b. What is the probability that none of the four spark plugs will fail during the first 20 minutes of flight?
c. What is the probability that at least one of the spark plugs will fail?