Jason referenced a very interesting article that I read at lengths which summed up my problem with such probability arguments http://www.straightdope.com/classics/a3_189.html. The original Monty and which door argument boils down into, well, yeah, what if, this or that.

If we have to teach probability then I would like it to be taught in the context of a computer. Talk about randomizing and then creating the algorithms to illustrate what the probabilities are. That way you can plug in real life found statistics and see what the probability actually is. Students have the power to simulate situations and scenarios that are nearly impossible to calculate using continous maths.

The Black-Sholes model is not really what I had in mind. I don’t like to use Black-Sholes because it makes too many assumptions and ignores the volatility smile. The Black-Sholes model also reminds me of the era where we did not have computing power. I tend to prefer discrete math like binomial, tri-nomial or jump pricing of options. Granted they make some assumptions, but at least you could simulate conditions and tweak the tree to test other thesis.

I guess what bugs me is the same thing that bugs people like Wolfram (A New Kind of Science) in that we are using continous mathematics that makes many assumptions. We have the power of computers so why not base our maths on discrete mathes that are more accurate and can be used to simulate? This is why I find the book Evidence Based Technical Analysis absolutely amazing.

For those wondering what discrete and continous math is read the wikipedia entry: http://en.wikipedia.org/wiki/Discrete_math.

The math examples that you gave are supposed to teach about how to use the values for the probability of single events to calculate cumulative probabilities, nothing more. The probabilities are assumed to be known. In real life, of course the probabilities are not known, they are assessed. But that does not make the principle of cumulative probability or the examples that illustrate it any less valid.

As far as the scientific method is concerned, I am sure it can be useful. However, one needs to be aware of certain things, like the assumptions made in the scientific model - in your case I presume the Black-Sholes model. The conditions under which it is valid are rigorously defined and hold for some sort of perfect market. I view it all like the ideal gas equation - it’s not really valid most of the time, but it gives good approximations under certain conditions. The real danger lies inplugging the numbers wihtout being aware of those conditions all the time.

Nice link to the coin tossing article. Problem though - the face that will be face up is random. Bias gone… unless you use a penny it seems.

:)

Phil