Lyme disease is the leading tick-borne disease in the United States and Europe. Diagnosis is difficult and is aided by a test that detects particular antibodies in the blood.
A study of 1000 people at risk for Lyme disease showed the results of the blood test, sorted by whether or not the patient actually had Lyme disease. Use the table to answer the questions that follow.
Patient has
Lyme disease
Patient does not
have Lyme disease
Total
Positive Test
19 10 29
Negative Test 1 970 971
Total 20 980 1000
Round all percentages to the nearest tenth.
(a) What percent of patients actually had Lyme disease?
Answer
2.0
%
(b) What percent of patients tested positive for Lyme disease?
Answer
1.9
%
(c) What percent of patients with Lyme disease tested positive? Hint: this is a conditional probability: the probability that a patient tested positive, given that they have Lyme disease.
Answer
1.9
%
(d) What percent of patients without Lyme disease tested negative? Hint: this is a conditional probability: the probability that a patient tested negative, given that they do not have Lyme disease.
Answer
97.0
%
(e) Most of the time, we don't know whether a patient has Lyme disease or not. If a patient had a positive test result, what is the probability that the patient actually had Lyme disease?
Answer
2.0
%