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Unformatted text preview: 1.13 Problems 51 Section 1.6: Properties of Probability 1.25 Mark and Lisa registered for Physics 101 class. Mark attends class 65% of the time and Lisa attends class 75% of the time. Their absences are inde- pendent. On a given day, what is the probability that (a) at least one of them is in class? (b) exactly one of them is in class? (c) Mark is in class, given that only one of them is in class? 1.26 The probability of rain on a day of the year selected at random is 0.25 in a certain city. The local weather forecast is correct 60% of the time when the forecast is rain and 80% of the time for other forecasts. What is the probability that the forecast on a day selected at random is correct? 1.27 53% of the adults in a certain city are female, and 15% of the adults are unemployed males. (a) What is the probability that an adult chosen at random in this city is an employed male? (b) If the overall unemployment rate in the city is 22%, what is the proba- bility that a randomly selected adult is an employed female? 1.28 A survey of 100 companies shows that 75 of them have installed wireless local area networks (WLANs) on their premises. If three of these compa- nies are chosen at random without replacement, what is the probability that each of the three has installed WLANs? Section 1.7: Conditional Probability 1.29 A certain manufacturer produces cars at two factories labeled A and B. Ten percent of the cars produced at factory A are found to be defective, while 5% of the cars produced at factory B are defective. If factory A pro- duces 100,000 cars per year and factory B produces 50,000 cars per year, compute the following: (a) The probability of purchasing a defective car from the manufacturer (b) If a car purchased from the manufacturer is defective, what is the prob- ability that it came from factory A? 1.30 Kevin rolls two dice and tells you that there is at least one 6. What is the probability that the sum is at least 9? 1.31 Chuck is a fool with probability 0.6, a thief with probability 0.7, and neither with probability 0.25. 52 Chapter 1 Basic Probability Concepts (a) What is the probability that he is a fool or a thief but not both? (b) What is the conditional probability that he is a thief, given that he is not a fool? 1.32 Studies indicate that the probability that a married man votes is 0.45, the probability that a married woman votes is 0.40, and the probability that a married woman votes given that her husband does is 0.60. Compute the following probabilities: (a) Both a man and his wife vote. (b) A man votes given that his wife does. 1.33 Tom is planning to pick up a friend at the airport. He has figured out that the plane is late 80% of the time when it rains, but only 30% of the time when it does not rain. If the weather forecast that morning calls for a 40% chance of rain, what is the probability that the plane will be late?...
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This note was uploaded on 01/05/2010 for the course STAT 350 taught by Professor Carlton during the Fall '07 term at Cal Poly.
- Fall '07