This is an interesting question. I would say that if you really do have complete 'direct knowledge about the mechanisms that can cause the event', then probability is not relevant. If you really do know enough about the die and its environment, including how it is propelled, then the problem of predicting the result of a toss is deterministic. It is because we do not have such complete knowledge that we have to resort to probability.
I could be cute and say that there is nothing certain about probability! With regard to your last questions, probability is not a 'phenomenon' but a way of modelling a situation in the absence of (deterministic) information. A probability model is essentially simply a listing of all the possible outcomes to be taken into account, with a probability for each. Literally ANY set of probabilities, provided it satisfies the basic rules, is legitimate. Whether it is appropriate, or useful, in a particular case is of course a very different matter. To obtain a useful set of probabilities you take into account any information you have. This might involve historical data, some knowledge of the underlying mechanisms, intuition, personal bias, ....... Have fun. Alan Bj�rn wrote: > > Estimating the probability for an event can be done in two ways: > > 1) Using historical data about the frequency of the event. > 2) Using direct knowledge about the mechanisms that can cause the > event. > > Examples: > - The probability for lung cancer as death cause for a smoker can be > estimated from the death rate of other smokers (approach 1). > - The probability for getting a 6 when casting a die can be calculated > from our knowledge about the geometry of the die and its environment > (approach 2). > > Of course, the probability for getting a 6 can be estimated by looking > at historical casts of dice, and lung cancer might be calculated from > our knowledge about the lungs, the immune system, the tobacco smoke > etc. The latter would be quite cumbersome since it would be very > complicated. > > What I wonder is, are these two approaches, 1 and 2 above, really > distinctly different? Are there other approaches? What are the > implications of using either? What if the two approaches yield > different estimates for the same event? How come that the same > phenomena, the probability, can be deduced by two so very different > approaches? > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102 Fax: +61 03 9903 2007 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
