Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is classified as conforming (suitable for its intended use), downgraded...

Three times each day, a quality engineer samples a component from a recently manufactured batch and tests it. Each part is classified as conforming (suitable for its intended use), downgraded (unsuitable for the intended purpose but usable for another purpose), or scrap (not usable). An experiment consists of recording the categories of the three parts tested in a particular day. a) List the 27 outcomes in the sample space. b) Let A be the event that all the parts fall into the same category. List the outcomes in A. c) Let B be the event that there is one part in each category. List the outcomes in B. d) Let C be the event that at least two parts are conforming. List the outcomes in C. e) List the outcomes in A ∩ C. f) List the outcomes in A ∪ B. g) List the outcomes in A ∩ C^c. h) List the outcomes in A^c
∩ C. i) Are events A and C mutually exclusive? Explain. j) Are events B and C mutually exclusive? Explain.