Question

4.3 Heart attack is one of the leading causes of death in many countries and cigarette smoking is the most preventable risk factor for heart attack. In a particular population, 20% of people suffered a heart attack, 16% of people are current smokers, and 12% of people had a heart attack while they were smokers. Let event A be a person who is a current smoker and event B be a person who had heart attack a) Construct a Venn diagram to show the relationship between having a heart attack and current smoking. b) Calculate P(A), P(B), P(AB), and P(ÄB). c) If a person is randomly selected from current smokers, what is the probability that this person would suffer a heart attack? d) If a person is randomly selected from current non-smokers, what is the probability that this person would suffer a heart attack? e) What is the risk of having a heart attack for current smokers? What is the risk of having a heart attack for current non-smokers f) What is the relative risk of suffering a heart attack for current smokers compared to currernt non-smokers? What is the relative risk comparing current non-smokers to current smokers? B) What are the odds of having a heart attack among those who are current smokers? What are the odds of having a heart attack among current non-smokers? h) What is the odds ratio of having a heart attack for current smokers compared to current non smokers? What would be the odds ratio comparing current non-smokers to current smokers?

Answer 1

4.3)

According to the question, $P(A)=0.16,P(B)=0.20,P(A\cap B)=0.12$

a)

Venn diagram is given by:

Current Smoker Heart Attack 16% 20% 12%

b)

From the given information, P(A) = 0.16, P(B) = 0.20,

$P(AB)=P(A\cap B)=0.12$

$P(\overline{A}B)=P(B)-P(A\cap B)=0.20-0.12=0.08$

c)

Required probability = $P(B|A)=\frac{P(B\cap A)}{P(A)}=\frac{0.12}{0.16}=0.75$

d)

Required probability = $P(B|A')=\frac{P(B\cap A')}{P(A')}=\frac{P(B)-P(B\cap A)}{1-P(A)}=\frac{0.20-0.12}{1-0.16}=0.0952$