Friday, July 4, 2008

Calling All Math Nerds....err, Mathletes

So, I'm currently reading this book which is one of the most thought provoking books I've ever read. I e-mailed my older brother one of the sections from the book and it led to a vigorous and animated discussion. During the course of the argument, we started thinking about a math problem and neither of could solve it on the spot. Having given it some thought, I've come up wiht my solution and have recreated it for all of you with the hopes that you might be able to show me if and where I've gone wrong.

Assume that we have a two person population, STD+ and STD-, with STD+ composing 75% of the population and STD- = (1-STD+). Given that we have a two person population, there are three kinds of interactions that can occur:

1) STD+/STD+
2) STD-/STD-
3) STD+/STD-

Our goal is to figure out how many NEW STD+ people there will be at the end of the night assuming that all individuals successfully couple with another individual, no discrimination or preferences are evident, the STD is 100% contagious and that there is no use of STD prevention devices.

The first two couplings are irrelevant because they do not create any new STD+. Only in the third coupling will there be a new STD+ person. With this in mind, it should be easy to compute.

1) (.75)(.75)= .5625
2) (.25)(.25)= .0625
.5625 + .0625= .625
1-.625= .375

So, in a 1,000 person population constrained by our above conditions, there will be 375 new STD+ people created.

Seem right?

edit: Studly reader Mark R has written in with what seems to be the correct solution. Read the comments to see what he has to say...


mark.r said...

"So, in a 1,000 person population constrained by our above conditions, there will be 375 new STD+ people created."

That can't be right, because there were only 250 STD- people in the first place. You're double-counting the interactions.

Here's another way to think of it. There are 250 STD- people. 3/4 of them sleep with STD+ people. .75 * 250 = 187.5.

Btw, if your model is headed where I think it is, you probably need to model the female and male populations separately.

Mike Czyzewski said...
This comment has been removed by the author.
Mike Czyzewski said...

thanks for writing in!

i understand your point about how the new STD+ population can't be bigger than the original STD- population...i felt really dumb after I read that and realized the sheer idiocy of my original conclusion. Thanks for pointing out an extremely easy way to come up with the (real) solution.

And no, my model isn't going anywhere. This is something I thought about for fun.

mark.r said...

you're welcome.

btw, i like your blog a lot. i know nothing about cooking, so your pictures and step-by-step instructions are really helpful and entertaining for me.

Mike Czyzewski said...

Glad you like the blog! I write my blog primarily to show people who don't cook, such as yourself, that cooking really isn't THAT hard. If I can get one person who otherwise wouldn't cook to cook a meal, I have been successful!