(January 7, 2015 at 10:55 pm)Heywood Wrote: You do not understand what probability is.I think you are confusing probability and likelihood.
Probability is not some established fact. The bag was either filled with all white marbles or it was not. The composition of the bag is a fact....and it happens to be unknown to us.
Probability is an estimate of how likely one particular set of circumstances has occurred or will occur. Because it is an estimate, it changes as available information changes. Each time you draw a marble from the bag, you obtain new information about the composition of the bag. This new information allows you to revise your estimate.
As you said, the bag contains all white marbles or it doesn't. If we know how the bag was filled we can calculate a probability that filling the bag will result in a bag of all white marbles. Observing the contents of the bag is not a causal event as related to the types of marbles it contains; therefore, it does not influence the probability of the bag containing all white marbles. Note here that observing the marbles one at a time or dumping them all out at once for observation has no effect on the probability of occurrence.
Likelihood on the other hand more accurately describes what you are attempting to convey. And no, likelihood and probability are not synonymous. If your bag contains 100 marbles, you are much more likely to have a bag of all white marbles after pulling 99 white marbles than you were after pulling the second. In this case, likelihood is a qualitative evaluation. Again, this has no influence on the probability of your bag containing all white marbles.
