1. ## Sampling of a General Population Probability question

Here's my homework question, my work/thoughts on it thus far are below the question.

A life insurance application asks the question "Are you a smoker?" The percentage of smokers in the general population is 15%. Furthermore, 40% of applicants who are smokers lie on the application, and say that they are non-smokers, but none of the non-smokers lie on the application. What proportion of applicants who say they are non-smokers are actually non-smokers?

Now, if the general population were the entire applicant pool, this would be really simple:
X = general population
.15X = Number of actual smokers
.4(.15X) = Number of smokers who said they were non smokers
.85X-(.4(.15X)) = Number of non-smokers polled who are actually non smokers.

But, seeing as this is for my college-level probability class and it doesn't say that the pool of applicants is in fact the general population, I feel like I'm missing something here. Does this have to do with conditional distribution and expectation values? Or am I overthinking this? Any hints or nudges in the right direction would be greatly appreciated!

2. ## Re: Sampling of a General Population Probability question

But, seeing as this is for my college-level probability class and it doesn't say that the pool of applicants is in fact the general population,
Good point, and in most practical situations its very likely that smokers will be over-represented in applications for life cover. This is because compared to the general population, they are more likely to die and hence have more to gain from the policy (depending on how it is priced).

However for the purpose of a probability class, i think you are expected to assume that 15% of applications are in fact from smokers.

.85X-(.4(.15X)) = Number of non-smokers polled who are actually non smokers.
You need a proportion, rather than a number. And im not sure you have calculated your number properly either. The number of people who are actually non smokers is 0.85X, and the number of people claiming to be nonsmokers is 0.85X plus 0.4(0.15X).

Its likely you were taught conditional probability formula before being set this question, try using that.