STUDENT FINANCIAL AID The accompanying data were obtained from the financial aid office of a certain university: Let A be the event that a student selected at random from this university is an undergraduate student, and let B be the event that a student selected at random is receiving financial aid. a. Find each of …

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EMPLOYEE EDUCATION AND INCOME The personnel department of Franklin National Life Insurance Company compiled the accompanying data regarding the income and education of its employees: Let A be the event that a randomly chosen employee has a college degree and B the event that the chosen employee’s income is more than $50,000. a. Find each …

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Two cards are drawn without replacement from a wellshuffled deck of 52 cards. Let A be the event that the first card drawn is a heart, and let B be the event that the second card drawn is a red card. Show that the events A and B are dependent events.

MEDICAL RESEARCH A nationwide survey conducted by the 8.2 CONDITIONAL PROBABILITY AND INDEPENDENT EVENTS 483 National Cancer Society revealed the following information. Of 10,000 people surveyed, 3200 were “heavy coffee drinkers” and 160 had cancer of the pancreas. Of those who had cancer of the pancreas, 132 were heavy coffee drinkers. Using the data in …

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SWITCHING INTERNET SERVICE PROVIDERS (ISPS) According to a survey conducted in 2004 of 1000 American adults with Internet access, one in four households plans to switch ISPs in the next 6 months. Of those who plan to switch, 1% of the households are likely to switch to a satellite connection, 27% to digital subscriber line …

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RELIABILITY OF SECURITY SYSTEMS Before being allowed to enter a maximum-security area at a military installation, a person must pass three independent identification tests: a voice-pattern test, a fingerprint test, and a handwriting test. If the reliability of the first test is 97%, the reliability of the second test is 98.5%, and that of the …

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RELIABILITY OF A HOME THEATER SYSTEM In a home theater system, the probability that the video components need repair within 1 yr is .01, the probability that the electronic components need repair within 1 yr is .005, and the probability that the audio components need repair within 1 yr is .001. Assuming that the events …

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PROBABILITY OF TRANSPLANT REJECTION The probabilities that the three patients who are scheduled to receive kidney transplants at General Hospital will suffer rejection are ½,1/3, and 1/10, Assuming that the events (kidney rejection) are independent, find the probability that a. At least one patient will suffer rejection. b. Exactly two patients will suffer rejection.

QUALITY CONTROL Copykwik has four photocopy machines: A, B, C, and D. The probability that a given machine will break down on a particular day is Assuming independence, what is the probability on a particular day that a. All four machines will break down? b. None of the machines will break down?

PRODUCT RELIABILITY The proprietor of Cunningham’s Hardware Store has decided to install floodlights on the premises as a measure against vandalism and theft. If the probability is .01 that a certain brand of floodlight will burn out within a year, find the minimum number of floodlights that must be installed to ensure that the probability …

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