he marketing department in the computer company is studying the pattern of the stores’ orders for better understanding of the customers’ needs. Some of the study findings are: 50% of the customers buy hardware products, while 50% buy software products. There is a 40% probability that a customer is interested in computer gaming, if he/she buys a hardware product. The probability that a customer buys a software product and is a computer programs developer is 30%. Based on this information, find the following: The probability that a random customer is interested in computer gaming and buys hardware products. The probability that a random customer is a computer programs developer if they buy software products. The probability that 6 out of the next 11 new customers are buying hardware products. Consider that the company inco

he marketing department in the computer company is studying the pattern of the stores’ orders for better understanding of the customers’ needs. Some of the study findings are: 50% of the customers buy hardware products, while 50% buy software products. There is a 40% probability that a customer is interested in computer gaming, if he/she buys a hardware product. The probability that a customer buys a software product and is a computer programs developer is 30%. Based on this information, find the following: The probability that a random customer is interested in computer gaming and buys hardware products. The probability that a random customer is a computer programs developer if they buy software products. The probability that 6 out of the next 11 new customers are buying hardware products. Consider that the company inco

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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More and more households are struggling to pay utility bills given a shaky economy and high heating costs (The Wall Street Journal, February 14, 2008). A representative sample of 500 households was taken to investigate if the type of heating influences whether or not a household is delinquent in paying its utility bill. The following table reports the results. If a household uses natural gas or propane, what is the probability it is delinquent ("Yes") in paying its utility bill. (Round answers to three decimal places.) Type of Heating Delinquent Natural Heating in Payment? Gas Electricity Oil Propane Yes 50 20 15 10 No 240 130 20 15
R4.1. Quality control A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect- something that does not work properly-and that 2% of new cars have both kinds of problems. a) If you buy a new car, what's the probability that it has some kind of defect? b) What's the probability it has a cosmetic defect but no functional defect? c) If you notice a dent on a new car, what's the probability it has a functional defect? d) Are the two kinds of defects disjoint events? Explain. e) Do you think the two kinds of defects are independent events? Explain.
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $40,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the investment will result in a loss of $40,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment?
1. The American Journal of Public Health (July 1995) published a study of the relationshipbetween passive smoking and nasal allergies in Japanese female students. The study revealedthat 80% of students from heavy-smoking families showed sign of nasal allergies on physicalexaminations. Consider a sample of 25 Japanese female students exposed daily to heavysmoking. d. What is the probability that more than 15 of the students will NOT have nasal allergies?e. What is the probability that more than 15 but fewer than 20 will have nasal allergies?
1. Researchers are interested in the relationship between vaping and upper respiratory infections. Suppose that 15% of their population of interest has vaped in the past year and 25% have had an upper respiratory infection in the past year. In addition, they know that 10% have both vaped and had an upper respiratory infection in the past year. What percent of the population has neither vaped nor had an upper respiratory infection in the past year? b. What is the probability of having an upper respiratory infection in the past year given that the person has vaped in the past year? What is the complement of the event in part b)? Be sure to interpret this probability in the context of the problem. a. C. d. What is the probability of having an upper respiratory infection in the past year given that the person has not vaped in the past year? Are the two events independent? Be sure to justify your answer. Based on your calculations what can you conclude about the relationship between vaping…
Virtually any process can be improved by use of statistics, including the law. A much publicized case that involved a debate about probability was the Collins case, which began in 1964. An incident of purse snatching in the Los Angeles area led to the arrest of Michael and Janet Collins. At their trial, an "expert" presented the probabilities listed in table below on characteristics possessed by a couple seen running from the crime scene: Characteristics Probability Man with beard 1/10 Blond woman 1/4 1/10 Yellow car Woman with ponytail Man with moustache Interracial couple 1/10 1/3 1/1000 The chance that a couple had all these characteristics together is 1 in 12 million. Because the Collinses had these characteristics, the Collinses must be guilty. Do yo see any problem with this line of reasoning? Hint: The question of interest is not "what is the probability of finding a couple with these characteristics?" because one such couple has been found (the Collinses), the question is "what…
2. The following table shows the income distribution for two groups of people in a country: those who declare to belong to a faith, and those who declare to be free thinkers. Income bracket Middle 13278 2225 Religious outlook Faith believer Free thinker Lower 7940 1241 Upper 4527 813 (a) A person is randomly selected from the group, find the probability that this person is a (i) free thinker. (ii) free thinker given that he/she has middle income. (iii) faith believer or he/she has lower income. (b) Are the events "Free thinker" and "Middle income" independent? Explain your answer. (Note: Round the probabilities to two significant figures)
6. An actuary studying the insurance preferences of automobile owners makes the following conclusions: (i) An automobile owner is twice as likely to purchase collision coverage as disability coverage. (ii) The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage. (iii) The probability that an automobile owner purchases both collision and disability coverages is 0.15. (a)Calculate the probability that an automobile owner purchases neither collision nor disability coverage. (b) Calculate the probability that an automobile owner purchases only collision coverage.
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $40,000. If the economy grows at a moderate pace, the investment will result in a profit of $20,000. However, if the economy goes into recession, the investment will result in a loss of $40,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment?