1. A test indicates the presence of a particular disease 90% of
the time when the disease is present and the presence of the
disease 2% of the time when the disease is not present. If 0.5% of
the population has the disease, calculate the conditional
probability that a person selected at random has the disease if the
test indicates the presence of the disease.
2. There is a new diagnostic test for a disease that occurs
in about 0.05% of the population. The test is imperfect, and it
will detect a person with the disease 99% of the time. However, it
will, say that a person without the disease has the disease three
out of 100 times. An individual is selected at random from the
population, and the test indicates that this individual has the
disease. Find the conditional probabilities that
(a) the person has the disease?
(b) the person does not have the disease?
3. At a hospital’s emergency unit (EU), patients are classified
by their degree of seriousness of the conditions. 20% of them are
classified as critical, 30% are serious, and 50% are stable. Of the
critical ones, 30% pass away; of the serious, 10% do not survive;
and of the stable ones, 1% die. Given that a patient dies, find is
the conditional probability that the patient was classified as
critical?
4. A doctor Is investigating the relationship between blood
pressure and irregular heartbeats. The doctor classifies her
patients’ blood pressures as high, normal, or low and
heartbeats as regular or irregular and she has found that
(a) 16% have high blood pressure;
(b) 19% have low blood pressure;
(c) 17% have an irregular heartbeat;
(d) of those with an irregular heartbeat, 35% have high blood
pressure; and
(e) of those with normal blood pressure, 11% have an irregular
heartbeat. percentage of her patients having regular heartbeats and
low blood pressure?
Find the percentage of her patients having regular
heartbeats and low blood pressure?