Tables are turning

In high school, I was fully convinced that I’m good in math, because I did well on our subjects (even when I’m not the best at it), and I actually enjoyed what we’re doing – the rush you get when doing simple computations, the awe of learning how simple things turn out to be, etc. College changed that. There came a time where my (academic) confidence was down so low that I always had to resort in group studies, but still ending up where I’m the one demo-ing for the group. :P

My confidence did dive permanently lower from where it it was. I’m good with it. And here goes my story.

This morning, I was doin my usual routine of studying for the upcoming SOA P (CAS 1) Exam and I was answering modules to practice. I’m already at the last part of the series of questions and they were basically harder than those of the first half. Reading the almost-last question gave me chills. The question is so interesting – it seemed easy, but I argued to myself that a question placed on the latter part of a set is sure to be challenging. I tried answering the question using what I thought as basic knowledge and entered many digits in my calculator. (I swear I know what I’m doing that moment, but most of it I know are right but I cannot explain why.) As I got the result, I checked it with the multiple choices and one of them matched. I’m lucky. I’m not convinced it’s correct; SOA exam multiple choices are designed to still have the answer you thought was right.

I checked the answer from the key and… my answer is correct. I wrote my solution and tried explaining what I did. It was simple. My solution is a two-liner equation with a Venn diagram as guide. I’m happy. :)

When I checked the solution from the key, I was shocked to see that it nearly used a whole (letter-sized) page! It was so complicated that I only understood it when it was streamlined, but still ferocious-looking at it. I didn’t bother digging up it’s calculations since the flow of the module’s solution resembled mine, and I’m happy turning for the next question.

I felt I was back in high school. Those were the times I would argue with my classmates because of math. I missed our reviews for math contests then, but the feeling during those time relived within me for a few minutes today.

PS For those interested, here’s the question:

One of the questions asked by an insurer on an application to purchase a life insurance policy is whether or not the applicant is a smoker. The insurer knows that the proportion of smokers in the general population is 0.30, and assumes the this represents the proportion of applicants who are smokers. The insurer has also obtained information regarding the honesty of applicants: 40% of applicants that are smokers say that they are non-smokers on their application while none of the applicants who are non-smokers lie on their application. (Obviously, hehe.) What proportion of applicants who say they are non-smokers are non-smokers indeed?

ANSWER: