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!