Exam 4: Probability

A market research firms conducts studies regarding the success of new products.The company is not always perfect in predicting the success.Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail).In the past, for all new products that ultimately were successful, 80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures).Also, for all new products that were ultimately failures, 70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes).For any randomly selected new product, what is the probability that the market research firm would predict that it would be a success?

In a set of 12 aluminum castings, two castings are defective (D), and the remaining ten are good (G).A quality control inspector randomly selects three of the twelve castings with replacement to test.The sample space for selecting the group to test contains __________ elementary events.

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A $\cup$ F)= _____________.

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (B|A).