In order to ensure the quality of concrete material used in a reinforced concrete construction, concrete cylinders are collected at random for concrete mixes delivered to the construction site by a mixing plant. Past records of concrete from the same plant show that 80% of concrete mixtures are of satisfactory quality. To further insure that the concrete delivered on site is of good quality, the engineer requires that one cylinder among those collected each day to be tested for 7-day compressive strength. The method's reliability is 90%. That is, the probability that a good quality concrete will pass the test is 0.90, while the probability that a poor-quality cylinder will pass the test is 0.10. a. Define all events of interest. (3 pts.)
b. Extract all relevant information from the problem using the notation in 7(a). (6 pts.)
c. Provide a graphical representation of the sample space. (10 pts.)
d. Use set notation to describe all outcomes in the sample space. (5 pts.)
e. If a concrete cylinder passes the test, what is the probability that good-quality concrete was delivered on site? (8 pts.)
f. What is the probability that a cylinder either fails the test or is of good quality? (8 pts.)