In the biomedical engineering field, a study of coronary artery disease had three possible partitioning events: B_1= the event that a person has critical coronary artery disease, B_2= the event that a person has noncritical coronary artery disease, B_3= the event that a person has negligible coronary artery disease. The prior probabilities, based on relative frequencies, are
P(B_1 )=0.10,P(B_2 )=0.70,P(B_3 )=0.20. The testing device is called a negative dipyrdamole thallium scan and if it is negative there is no coronary artery disease. The testing device can either be positive or negative. Let A be the event that the testing device is negative. The conditional probabilities are P(A?B_1 )=0.05,P(A?B_2 )=0.20,P(A?B_3 )=0.88. Find the
a) Probability a person has negligible coronary artery disease and the testing device is negative
b) Probability a person has critical coronary artery disease given the testing device is negative
c) Probability the testing device is positive, d) probability the testing device is negative
e) Probability a person has noncritical coronary artery disease, given the testing device is positive. (a false positive for a person who has noncritical coronary artery disease)