Posts Tagged ‘probability’

Carnival of Mathematics #53 is up!

June 5, 2009

As promised earlier, the Carnival of Mathematics #53 is up at The Math Less Traveled.    It has a healthy number of posts on topics from brain exercises to hyperbolic models to Sangaku and GeoGebra.    The Carnival may be  a bit unpredictable these days, but it’s good to see that it’s just as fun to read!

Speaking of Carnivals, we went to one tonight — a real live one.  And we did the Cake Walk (and won some vivid cupcakes that might be interesting to view under a black light to see if they would glow), but before doing it I did a quick estimate as to whether it was better for four of us to play in a single 10-person game, or to spread it out over more than one game [two going in one round and two going in another].  This is similar to the Box Top problem, but has a different answer because the number of people per round is fixed:  the expected number of wins is the same whether or not we all go in the same round, but we’re more likely to win at least once if we all go at the same time.   In particular, although we lose the possibility of winning more than once by going in the same round, that’s offset by an increase in the probability that we’ll win at least once.  (I find it interesting that it has a different answer than the Box Top problem, which I still don’t feel 100% settled about.)

From Aliens to Supermodels

April 22, 2008

There was an article Saturday on Science Digest about the odds of finding life on other planets: according to Andrew Watson (an Environmental Science professor at the University of East Anglia), life evolved fairly late in the game here on Earth, which suggests that it is more unlikely than likely to evolve on other planets. I found this rather depressing, but consoled myself with the notion that these kinds of probabilities are just guesswork anyway. After all, Dr. Frank Drake came up with his own equation in 1960 that (according to Wikipedia) suggests there are 10 civilizations in our galaxy that we might be able to communicate with. Of course, not everyone liked that equation either.

Thinking about calculating difficult odds reminded me of one of my favorite light books on the subject: Life: the Odds (and How to Improve Them) by Gregory Baer. It appears to be out of print (looking at Amazon) but if you find a copy, it contains calculations of the odds of unlikely events such as marrying royalty (500 to 1 in the UK, with better odds for marrying male royalty than female), being audited (175 to 1 in just the year 2002; about 3 to 1 over a lifetime), and hitting a hole in one (12,000 to 1). What’s more intriguing to me than the actual odds is the reasoning that went into the calculations. Gregory, like Frank, had to make guesses for some numbers (and made some clearly incorrect assumptions, like that everyone is hetero- or bisexual), but it’s still interesting to see the details of just where those numbers come from.

You can see those thought processes on a couple places online: the first chapter, Dating a Supermodel, is reproduced in full, while this ABC News article gives a summary of calculating several of the odds in the book.

The thumbnail of Spiral Galaxies in Collision was the Astronomy Picture of the Day on April 20, 2008. Have you ever seen APOD? It’s got some amazing pictures!