(January 7, 2015 at 11:33 pm)Jenny A Wrote:(January 7, 2015 at 11:19 pm)JuliaL Wrote: Hang on a minute.
I'm going either to be pedantic or dim.....or dimly pedantic.
But you have to specify something about the initial conditions for the marbles, for example, that the probability of any single marble of being white is 0.5 and black is the other 0.5.
No, it's an attempt to explain that we never know anything for sure unless we've seen it. It's disingenuous though because it suggests we make our scientific conclusions about the world based upon samples sizes as small as one or two. But you're quite right that assuming from the get go the the chances of black or white is 50/50 is unwarranted.
When I wrote out the example, I didn't spell out every assumption....like the overall distribution of colored marbles in the universe. So sure...if black marbles don't exist in the universe...the probability of drawing one from the bag is 0 and it is always going to be 0.
Now regarding scientific conclusions....we begin to draw conclusions the moment we observe and reflect and we do begin to make conclusions after just one observation. The number of observations just increases our confidence in those conclusions.
