A researcher finds that, of 982 men who died in 2002, 221 died from some heart disease. also, of the 982 men, 334 had at least one parent who had some heart disease. of the latter 334 men, 111 died from some heart disease. a man is selected from the group of 982. given that neither of his parents had some heart disease, find the conditional probability that this man died of some heart disease.

The question may be solved using the laws of total probability, Bayes theorem, conditional probability, etc. However, it is most readily solved by constructing a contingency diagram.

Events:

H=died of heart disease

~H=did not die of heart disease

P=at least one parent has heart disease

~P=no parent have heart disease

From given information, we can construct contingency diagram as follows:

H ~H Total

P 111 334

~P

Total 221 982

From the above diagram, we calculate

|~P & H| = 221-111=110

| P & ~H | = 334-111 = 223

Total | ~P | = 982-334=648

Total | ~H | = 982-221=761

| ~H & ~P | = 648-110 = 538

=>

H ~H Total

P 111 223 334

~P 110 538 648

Total 221 761 982

=>

P (H|~P) = 110/648=55/324

=0.170 (approx.)