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Homework answers / question archive / 1) A survey was conducted about the three hobbies, namely, reading books, watching movies, and listening to music

1) A survey was conducted about the three hobbies, namely, reading books, watching movies, and listening to music

Statistics

1) A survey was conducted about the three hobbies, namely, reading books, watching movies, and listening to music. The following statistics were cal-culated using a collection of 1,000 college students. Of them, 13%, 22%, and 36% read books, watch movies, and listen to music, respectively. Also, 7% of the students read books and watch movies; 8% read books and listen to music, and 12% watch movies and listen to music. Finally, 4% of the students do all the three hobbies. Using these pieces of information, answer the following questions:    (a) If a student is selected and he watches movies, what is the probability that he reads books, also?     (b)If a student is selected and she watches movies and listens to music, what is the probability that she also reads books?

2) It is known that 10% of new computers arriving at a computer store are defective of some type. Answer the following questions:    (a)Two computers of some new arrivals have been selected consecutively to check for defectiveness without replacement. What is the probability that the first computer is non-defective and the second is defective?    (b) If three computers are selected in the same way as in (i), what is the probability that the first and second are defective and third is non-defective?

3) Suppose Steve and his sister have motorcycles. The probability that Steve’s cycle has a mechanical problem is found to be 0.3, whereas the probability that his sister’s cycle has a mechanical problem is 0.4. Answer the following questions:   (a)What is the probability that both of motorcycles have mechanical problems?    (b) What is the probability that either Steve’s or his sister’s motorcycle has a mechanical problem?      (c)What is the probability that only one of the motorcycles has a mechanical problem?     (d)What is the probability that both of their motorcycles do not have mechanical problems?

4) A mechanic shop has three mechanics, identified as #1, #2, and #3. The percentage of all jobs assigned are 40, 35, and 25, to mechanics #1, #2, and #3, respectively. From the history of experience, the owner of the shop knows the probability of errors for each of the mechanics as 0.05, 0.03, and 0.03, for mechanics #1, #2, and #3, respectively. Answer the following questions:    (a)What is the probability that the service stations make a mistake with a given job?     (b) If a customer complains about a mistake in a prior completed job, who might have done the above mistake?

5) Consider a shipment of computers to an electronic store. Historical data indicates that a shipment of this type contains defects of different types. Here are the numbers: CPU only: 5%, RAM: 7%, and both CPU and RAM: 3%. To assess the defectiveness, a computer is selected randomly. Find the following probabilities regarding the selected computer:    (a) Only one type of defect,     (b)Both types of defects,     (c)Either CPU defect or RAM defect,     (d)Neither type of defects.

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