A randomly chosen person in a city claims to be healthy (event H1) with probability 0.75 and
unwell (event U1) otherwise. The city puts a person through the following treatment for a month. A person who
claims to be unwell is given a placebo (event B) with probability 0.25 and a get-healthy drug (event D) with
probability 0.75. On the other hand, a person who claims to be healthy is given a placebo with probability 0.75
and a get-healthy drug otherwise.
After a month of treatment as described above, the person is subject to a diagnostic test and also asked whether
the person feels healthy or unwell. Independent of the person’s initial claim about being healthy or unwell, the test
reports with probability 0.75 a person who was on a placebo to be unwell (define RU as the event that test reports
unwell) and reports with probability 0.75 a person who was on the get-healthy drug to be healthy (RH is the event
that the test reports healthy).
The diagnostic test has the following characteristics. It reports as unwell, a person who claims to be healthy post
treatment (event H2), with probability 0.1. It reports as unwell, a person who claims to be unwell (event U2), with
probability 0.9.
(a) Calculate the probability that a person is given the placebo.
(b) Calculate the probability that the test reports a person to be healthy.
(c) Calculate the probability that at the end of the treatment, a person whose test report says unwell, claims to be
healthy.
(d) Calculate the probability that at the end of the treatment, a person whose test report says healthy, claims to be
healthy.
(e) Calculate the probability that at the end of the treatment a person claims to be healthy.
(f) Suppose at the end of the treatment the person claims to be unwell. Calculate the probability that the person
claimed to be healthy before the treatment?