If I give you a die and ask about the probabiliy for a 6, then it's exactly 1/6. Being able to quantify this exactly is the great success story of probability theory. You can have a different "gut feeling", and indeed many people do (lotteries are popular), but you would be wrong. If you run this experiment a large number of times, then about 1/6 of the outcomes will be a 6, proving the 1/6 right and the deviating "gut feeling" wrong. That number is not "pulled out of somebody's ass" or some frequentist approach. It's what probability means.
I see, you don't know what I'm talking about. My apologies, I assumed a common background. Here's some introductory materials on Bayesian vs frequentist interpretations of probability:
Bayesian and frequentist reasoning in plain English
If I give you a die and ask about the probabiliy for a 6, then it's exactly 1/6. Being able to quantify this exactly is the great success story of probability theory. You can have a different "gut feeling", and indeed many people do (lotteries are popular), but you would be wrong. If you run this experiment a large number of times, then about 1/6 of the outcomes will be a 6, proving the 1/6 right and the deviating "gut feeling" wrong. That number is not "pulled out of somebody's ass" or some frequentist approach. It's what probability means.