A large study of lifestyle effects on heart disease yielded the following statis

Question

A large study of lifestyle effects on heart disease yielded the following statistics:

Smokers   40%

Obesity    30%

Heart Disease    10%

Smokers and Obese    20%

Smokers and Heart Disease    6%

Obese and Heart Disease    5%

Smoker, Obese and Heart Disease    4%

Which of the following is NOT a true statement?

Select one:

a. The probability that a randomly sampled individual from this population is a smoker and obese is 20%.

b. If a randomly chosen individual is obese, the probability that he/she has heart disease is 16.67%.

c. All of the answer choices are not true statements.

d. Heart disease and smoking are independent in this population.

e. The probability that a randomly sampled individual from this population is either a smoker or obese is 50%.

Explanation / Answer

P(heart disease given that he is obese)=P(heart disease and obese)/P(obese)=0.05/0.3=16.67%

P(heart disease and smoking)=0.06 , P(heart disease)=0.1 and P(smoking)=0.4, since P(heart disease and smoking) is not equal to  P(heart disease)*P(smoking)=0.1*0.4=0.04, thus they are not independent so answer D is the right option

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