Before leaving the factory, items are inspected to determine if they are good for use or defective (defective no or yes). Suppose 10 percent of items actually are flawed. If an item is flawed, the inspection process will label it as negative (-) with probability 0.9 (negative yes or no). If the item is not flawed, the inspection process will label it negative (-) with probability 0.05. Let F denote the event the item is flawed, and − denote the event the item is labeled as negative. So we have F for flawed and F c for not flawed, and − for negative and −c (or +) for not negative (positive). a. What is the probability a randomly chosen item is labeled negative -? b. An item is labeled negative -. What is the probability that the item is flawed (given it is labeled negative) c. Are the events F and − independent? Why or why not.

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-responsequestion. there are 15 questions on the test and the students have been given 55 minutes to complete itwhich value could replace x in the table? 5507-m23-m8(15-m)8(15)-m

The architect's side view drawing of a saltbox-style house shows a post that supports the roof ridge. the support post is 8 ft tall. the distance from the front of the house to the support post is less than the distance from the post to the back of the house. how far from the front of the house is the support post positioned?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)