Lyme disease is transmitted by infected ticks. Several tests are available for people with symptoms of Lyme dis- ease. One of these tests is the EIA/IFA test. The paper “lyme disease testing by large commercial laboratories in the united States” (Clinical Infectious Disease [2014]: 676–681) found that 11.4% of those tested actually had Lyme disease. Consider the following events: 1 represents a positive result on the blood test 2 represents a negative result on the blood test L represents the event that the patient actually has Lyme disease LC represents the event that the patient actually does not have Lyme disease The following probabilities are based on percentages given in the paper: P(L) 5 0.114 P(LC ) 5 0.886 P(1|L) 5 0.933 P(2|L) 5 0.067 P(1|LC ) 5 0.039 P(2|LC ) 5 0.961 a. For each of the given probabilities, write a sentence giv- ing an interpretation of the probability in the context of this problem. b. Use the given probabilities to construct a hypothetical 1000 table with columns corresponding to whether or not a person has Lyme disease and rows corresponding to whether the blood test is positive or negative. c. Notice the form of the known conditional probabilities; for example, P(1|L) is the probability of a positive test given that a person selected at random from the popula- tion actually has Lyme disease. Of more interest is the probability that a person has Lyme disease, given that the test result is positive. Use information from the table constructed in Part (b) to calculate this probability.
Lyme disease is transmitted by infected ticks. Several
tests are available for people with symptoms of Lyme dis-
ease. One of these tests is the EIA/IFA test. The paper
“lyme disease testing by large commercial laboratories in
the united States” (Clinical Infectious Disease [2014]: 676–681)
found that 11.4% of those tested actually had Lyme disease.
Consider the following events:
1 represents a positive result on the blood test
2 represents a negative result on the blood test
L represents the
Lyme disease
LC represents the event that the patient actually does not
have Lyme disease
The following probabilities are based on percentages given
in the paper:
P(L) 5 0.114
P(LC ) 5 0.886
P(1|L) 5 0.933
P(2|L) 5 0.067
P(1|LC ) 5 0.039
P(2|LC ) 5 0.961
a. For each of the given probabilities, write a sentence giv-
ing an interpretation of the
this problem.
b. Use the given probabilities to construct a hypothetical
1000 table with columns corresponding to whether or
not a person has Lyme disease and rows corresponding
to whether the blood test is positive or negative.
c. Notice the form of the known conditional probabilities;
for example, P(1|L) is the probability of a positive test
given that a person selected at random from the popula-
tion actually has Lyme disease. Of more interest is the
probability that a person has Lyme disease, given that
the test result is positive. Use information from the table
constructed in Part (b) to calculate this probability.
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