Question

Suppose that 23% of adults smoke cigarettes. It’s known that 57% of smokers and 13% of nonsmokers develop a certain lung condition by age 60.

a) Explainhowthesestatisticsindicatethatlungcondi- tion and smoking are not independent.
b) What’stheprobabilitythatarandomlyselected 60-year-old has this lung condition?

Answer 1

a) As explained in the question, 23% of adult population smokes cigarettes with 57% of them gets lung condition, while 77% adult population doesn't smoke cigarettes of which 13% get lung condition. So there is higher probability that lung condition and smoking are dependent.

b) After converting the values to probabilities and solving them we get that the probability for a random 60 year old person having a lung condition is 0.2312.

Explanation:

a) Converting percentages to probability as probability to smoking is 0.23, with 0.57 probability of getting lung condition. While the probability of having lung condition for non-smokers is 0.13.

As there is a 0.57 probability for smokers to get lung conditions(23% of whole adult population).

While there is 0.13 probability for non-smokers to get lung conditions(77% of whole adult population).

Thus it is concluded that most smokers get lung conditions. Thus lung conditions are dependent upon smoking.

b) Taking the probabilities for smokers as 0.23 of which 0.57 probability with lung conditions and 0.13 probability of remaining non-smokers with lung conditions.

Thus

For both smokers and non-smokers we multiply the probabilities and sum them up.

`=0.23*0.57+(1-0.23)*0.13`

`=0.2312`

So there is 0.2312 probability that a random selected 60 year old person have lung conditions.