Show work with explanation Maybe Venn Diagram use A public h

Show work with explanation: Maybe Venn Diagram use.

A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least on parent who suffered from heart diseases, and , of these 312 of the 937 men had at least one parent who suffered from heart disease, and of these 312 men, 102 died from causes related to heart disease, Determine the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease.

Solution

Let us call event of having heart disease, event A
& call event of no parental history of disease, event B

no. with heart disease = 210
P[A] = 210/937

no. with no parental history of disease = 937 - 312 = 625
P[B] = 625/937

no. from this group who died of heart disease = 210 - 102 = 108
P[A and B] = 108/937

required probability = P[A | B] = P[A and B] / P[B]
= [108/937] / [625/937] = 108 /625 = 0.1728 = 17.28 %