A chemical engineer is in charge of a particular process at an oil refinery. Past experience indicates that 10% of all shutdowns are due to equipment failure alone, 5% are due to a combination of equipment failure and operator error, and 40% involve operator error. A shutdown occurs. Find the probability that

(a) equipment failure or operator error is involved

(b) operator error alone is involved

(c) neither operator error nor equipment failure is involved

(d) operator error is involved given that equipment failure occurs

(e) operator error is involved given that equipment failure does not occur Are the events E: an operator error occurs, and F: an equipment failure occurs independent? Explain.