A certain patient can experience three different types of symptoms Let Ai (i = 1,2,3) denote the event that the patient has a symptom of type i. Suppose that the following probabilities are true.
P(A1) = 0.11 P(A2) = 0.07 P(A3) = 0.05
P(A1 ? A2) = 0.15 P(A1 ? A3) = 0.14
P(A2 ?A3) = 0.1 P(A1 ? A2 ? A3) = 0.01
(a) Given that the patient has a type 1 symptom, what is the probability that he has a type 2 symptom?
(b) Given that the patient has a type 1 symptom, what is the probability that he has all three types of symptoms?
(c) Given that the patient has at least one type of symptoms, what is the probability that it has exactly one type of symptom?
(d) Given that the patient has both of the first two types of symptoms, what is the probability that he does not have the third type of symptom?