# calculating probability and checking independence

Chapter 7 Sample Problems

41. A company has recently replaced their e-mail server because previously mail was interrupted on about 15% of workdays. To see how bad the situation was, calculate the probablity that during a 5-day work week, there would be an e-mail interruption. A) On Monday and again on Tuesday? b) For the first time on Thursday? c) Every day? d) At least once during the week?

51. Laptop computers have been growing in popularityaccording to a study by Current Analysis Inc. Laptops now represent more than half the computer sales in the United States. A campus bookstore sells both types and in the last semester sold 56% laptops and 44% desktops. Reliability rates for the two types of machines are quite different, however. In the first year, 5% of desktops require service, while 15% of laptops have problems requiring service. a) Sketch a probability tree for this situation. b) What percentage of computers sold by the bookstore last semester require service? c) Given that a computer require service, what is the probability that it was a laptop?

53. A 2011 Mintel report on coffeehouse asked consumers if they were spending more time in coffeehouse the table below gives the responses classified by age: a) What is the probability that a randomly selected respondent is spending more time at coffeehouse and donut shops this year than last year? b) What is the probability that the person is younger than 25 years old? c) What is the probability that the person is younger than 25 years old and is spending more time at coffeehouse and donut shops compared to last year? d) What is the probability that the person is younger than 25 years old or is spending more time at coffeehouse and donut shops compared to last year?

All 18-14 Yrs Old 25-34 Yrs Old 35-44 Yrs Old 45-54 Yrs Old 55-64 Yrs Old 65+ Yrs Old

Coffeehouse Survey

I am spending less time at coffehouses and donut shops this year than last year 499 78 93 102 104 68 48

I am spending about the same amount of time at coffehouses and donut shops this year as last year 522 82 109 106 89 75 67

I am spending more time at coffehouses and donut shops this year than last year 114 30 30 18 19 11 6

Total 1135 190 232 226 212 154 121

61. Look again at the data from the coffeehouses survey problem 53 above. A) If we select a person at random, what's the probability we choose a person between 18 and 24 years old who is spending more at coffeehouses? b) Among the 18- to 24-year olds, what is the probability that the person responded that they are not spending more at coffeehouses? c) What is the probability that the person who spends the same amount at coffeehouses is between 35 and 44 years old? d) If the peson responded that they spend more, what's the probability that they are at least 65 years old? e) What's the probability that a person at least 65 years old spends the same amount? f) Are the responses to the question and age independent?

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#### Solution Summary

The solution gives detailed steps on calculating probability for different events and then checking independence of two events.