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Chapter 7: Problem 23
Let \(S=\\{a, b, c\\}\) be a sample space of an experiment with outcomes \(a, b\), and \(c\). List all the events of this experiment.
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A study conducted by the Metro Housing Agency in a midwestern city revealed the following information concerning the age distribution of renters within the city. $$\begin{array}{lcc} \hline & & \text { Group } \\ \text { Age } & \text { Adult Population, \% } & \text { Who Are Renters, \% } \\\ \hline 21-44 & 51 & 58 \\ \hline 45-64 & 31 & 45 \\ \hline 65 \text { and over } & 18 & 60 \\ \hline \end{array}$$ a. What is the probability that an adult selected at random from this population is a renter? b. If a renter is selected at random, what is the probability that he or she is in the \(21-44\) age bracket? c. If a renter is selected at random, what is the probability that he or she is 45 yr of age or older?
In a survey to determine the opinions of Americans on health insurers, 400 baby boomers and 600 pre-boomers were asked this question: Do you believe that insurers are very responsible for high health costs? Of the baby boomers, 212 answered in the affirmative, whereas 198 of the pre-boomers answered in the affirmative. If a respondent chosen at random from those surveyed answered the question in the affirmative, what is the probability that he or she is a baby boomer? A pre-boomer?
The chief loan officer of La Crosse Home Mortgage Company summarized the housing loans extended by the company in 2007 according to type and term of the loan. Her list shows that \(70 \%\) of the loans were fixed-rate mortgages \((F), 25 \%\) were adjustable-rate mortgages \((A)\), and \(5 \%\) belong to some other category \((O)\) (mostly second trust-deed loans and loans extended under the graduated payment plan). Of the fixed-rate mortgages, \(80 \%\) were 30 -yr loans and \(20 \%\) were 15 -yr loans; of the adjustable-rate mortgages, \(40 \%\) were 30 -yr loans and \(60 \%\) were 15 -yr loans; finally, of the other loans extended, \(30 \%\) were 20 -yr loans, \(60 \%\) were 10 -yr loans, and \(10 \%\) were for a term of 5 yr or less. a. Draw a tree diagram representing these data. b. What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 15 yr? c. What is the probability that a home loan cxtended by La Crosse is for a term of 15 yr?
The admissions office of a private university released the following admission data for the preceding academic year: From a pool of 3900 male applicants, \(40 \%\) were accepted by the university and \(40 \%\) of these subsequently enrolled. Additionally, from a pool of 3600 female applicants, \(45 \%\) were accepted by the university and \(40 \%\) of these subsequently enrolled. What is the probability that a. A male applicant will be accepted by and subsequently will enroll in the university? b. A student who applies for admissions will he accepted by the university? c. A student who applies for admission will be accepted by the university and subsequently will enroll?
In an attempt to study the leading causes of airline crashes, the following data were compiled from records of airline crashes from 1959 to 1994 (excluding sabotage and military action). $$\begin{array}{lc} \hline \text { Primary Factor } & \text { Accidents } \\ \hline \text { Pilot } & 327 \\ \hline \text { Airplane } & 49 \\ \hline \text { Maintenance } & 14 \\ \hline \text { Weather } & 22 \\ \hline \text { Airport/air traffic control } & 19 \\ \hline \text { Miscellaneous/other } & 15 \\ \hline \end{array}$$ Assume that you have just learned of an airline crash and that the data give a generally good indication of the causes of airline crashes. Give an estimate of the probability that the primary cause of the crash was due to pilot error or bad weather.
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