In: Statistics and Probability
Imagine a population in the midst of an epidemic where 60% of
the population is considered susceptible, 10% are infected, and 30%
are recovered. There is only one test for the disease. For
susceptible patients the test is accurate (i.e. returns a negative
result) 95% of the time. For infected patients the test is correct
(i.e. returns a positive result) 99% of the time. The test is
correct (i.e. returns a negative results) 65% of the time for
recovered individuals.
a) Find the probability a patient actually is infected given they
received a positive test result. Circle your final answer. Hint: It
may be helpful to draw a tree diagram.
b) Are the events of “being susceptible” and “having a positive
test result” independent? Circle one of the options and provide
justification for your answer.
YES NO