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Bayes' Probability Exercises: P(A/B) and Related Calculations - Studocu ( )
6.72 Refer to Exercise 6.48. Find the fol owing. a. P(A/B) b. P(Ac/B) c. P(A/Bc) d. P(Ac/Bc)
6.73 Refer to Example 6.9. An MBA applicant believes that the probability of scoring more
than 650 on the GMAT without the preparatory course is .95. What
is the probability of at aining that level after taking the preparatory course?
6.74 Refer to Exercise 6.58. The plant manager randomly selects a molding from the early
morning run and discovers it is defective. What is the probability that the foreman forgot to
shut off the machine the previous night?
6.75 The U.S. National Highway Traffic Safety Administration gathers data concerning the
causes of highway crashes where at least one fatality has occurred. The fol owing
probabilities were determined from the 1998 annual study (BAC is blood-alcohol content).
(Source: Statistical Abstract of the United States, 2000, Table 1042.)
P(BAC =0 /Crash with fatality) = .616
P(BAC is between .01 and .09 /Crash with fatality) = .300
P(BAC is greater than .09/ Crash with fatality) = .084
Over a certain stretch of highway during a 1-year period, suppose the probability of being
involved in a crash that results in at least one fatality is .01. It has
been estimated that 12% of the drivers on this highway drive while their BAC is greater than .09.
Determine the probability of a crash with at least one fatality if a driver drives while legal y
intoxicated (BAC greater than .09).
6.76 Refer to Exercise 6.62. A randomly selected candidate who took a CFA exam tel s you
that he has passed the exam. What is the probability that he took the CFA I exam?
6.77 Bad gums may mean a bad heart. Researchers discovered that 85% of people who
have suffered a heart at ack had periodontal disease, an inflammation of the gums. Only
29% of healthy people have this disease. Suppose that in a certain community heart at acks
are quite rare, occurring with only 10% probability. If someone has periodontal disease,
what is the probability that he or she wil have a heart at ack? 08:49, 28/01/2026
Bayes' Probability Exercises: P(A/B) and Related Calculations - Studocu
6.78 Refer to Exercise 6.77. If 40% of the people in a community wil have a heart at ack,
what is the probability that a person with periodontal disease wil have a heart at ack?
6.79 Data from the Office on Smoking and Health, Centers for Disease Control and
Prevention, indicate that 40% of adults who did not finish high school, 34% of high school
graduates, 24% of adults who completed some col ege, and 14% of col ege graduates
smoke. Suppose that one individual is selected at random, and it is discovered that the
individual smokes. What is the probability that the individual is a col ege graduate? Use the
probabilities in Exercise 6.45 to calculate the probability that the individual is a col ege graduate.
6.80 Three airlines serve a smal town in Ohio. Airline A has 50% of al the scheduled
flights, airline B has 30%, and airline C has the remaining 20%. Their on-time rates are
80%, 65%, and 40%, respectively. A plane has just left on time. What is the probability that it was airline A?
6.81 Your favorite team is in the final playoffs. You have assigned a probability of 60%
that it wil win the championship. Past records indicate that when teams win the
championship, they win the first game of the series 70% of the time. When they lose the
series, they win the first game 25% of the time. The first game is over; your team has lost.
What is the probability that it wil win the series?
The fol owing exercises are based on the Applications in Medical
Screening and Medical Insurance subsection.
6.82 Transplant operations have become routine. One common transplant operation is for
kidneys. The most dangerous aspect of the procedure is the possibility that the body may
reject the new organ. Several new drugs are available for such circumstances, and the
earlier the drug is administered, the higher the probability of averting rejection. The New
England Journal of Medicine recently reported the development of a new urine test to
detect early warning signs that the body is rejecting a transplanted kidney. However, like
most other tests, the new test is not perfect. When the test is conducted on someone whose
kidney wil be rejected, approximately one out of five tests wil be negative (i.e., the test is
wrong). When the test is conducted on a person whose kidney wil not be rejected, 8% wil
show a positive test result (i.e., another incorrect result). Physicians know that in about 35%
of kidney transplants the body tries to reject the organ. Suppose that the test was performed
and the test is positive (indicating early warning of rejection). What is the probability that 08:49, 28/01/2026
Bayes' Probability Exercises: P(A/B) and Related Calculations - Studocu
the body is at empting to reject the kidney?
6.83 The Rapid Test is used to determine whether someone has HIV (the virus that causes
AIDS). The falsepositive and false-negative rates are .027 and .080, respectively. A
physician has just received the Rapid Test report that his patient tested positive. Before
receiving the result, the physician assigned his patient to the low-risk group (defined on the
basis of several variables) with only a 0.5% probability of having HIV. What is the
probability that the patient actual y has HIV?
6.84 What are the sensitivity, specificity, positive predictive value, and negative predictive
value in the previous exercise?
6.85 The Pap smear is the standard test for cervical cancer. The false-positive rate is .636;
the falsenegative rate is .180. Family history and age are factors that must be considered
when assigning a probability of cervical cancer. Suppose that, after
obtaining a medical history, a physician determines that 2% of women of his patient’s age
and with similar family histories have cervical cancer.
Determine the effects a positive and a negative Pap smear test have on the probability that
the patient has cervical cancer. 08:49, 28/01/2026
Bayes' Probability Exercises: P(A/B) and Related Calculations - Studocu