5.1.2. Consider people waiting in line to be tested for the certain virus that will not be named.
Let S denote the situation that a person has symptoms, and F denote the situation that a
person is symptom free. Let Y denote the event that a person has the virus and N the event
that the person does not have it. Suppose P(S) = 0.3, P(Y |S) = 0.2 and P(Y |F) = 0.01.
(a) Determine the probability that a random person waiting in line has the virus, P(Y ).
(b) Determine the conditional probability that a person has symptoms given that they
have the virus, P(S|Y ), and determine the conditional probability that a person has
symptoms given that they do not have the virus, P(S|N).