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entropy1

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- TL;DR Summary
- When are we sure we have the right probabilities?

If we have a jar with 3 blue balls and 7 white balls, we say that the probability of blindly getting a blue ball out of that jar is 30%. If we have a jar with 2 blue balls and 8 white balls, we say that the probability of blindly getting a blue ball out of it is 20%.

Now if we carry out 10 measurements out of a physical process that has 30% probability of yielding a blue outcome and 70% probability of yielding a white outcome, and we measure 2 blue outcomes and 8 white outcomes, can we then say that the probability of getting a blue outcome is 20% instead of 30%? In other words, when are we sure we have the right probabilities?

Now if we carry out 10 measurements out of a physical process that has 30% probability of yielding a blue outcome and 70% probability of yielding a white outcome, and we measure 2 blue outcomes and 8 white outcomes, can we then say that the probability of getting a blue outcome is 20% instead of 30%? In other words, when are we sure we have the right probabilities?