6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, it is known that the probability that machine A produces a defective component is 0.015 while the probability that machine B produces a defective component is 0.025. If a component is selected at random from a day's production, find the probability that the component is defective. If a component is selected at random from a day's production and is found to be defective, use Bayes' theorem to find the probability that it is made by machine A. а. b.

A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 16.5​% daily failure rate. a. What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam? ​(Round to three decimal places as​ needed.)   b. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?   ​(Round to five decimal places as​ needed.)   c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?   ​(Round to five decimal places as​ needed.)

The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up. a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0". No pooling: Pooling: 51.4 % 83.8 % b. Now suppose the numbers of people who show up at…