I think there’s some value in that observation that “the all 45 thing makes it feel like a trick”. I believe that’s a big part of why this feels like a paradox.
If you have a box with the numbers “60” and “20″ as described above, then I can see two main ways that you could interpret the numbers:
A: The number of coins in this box was drawn from a probability distribution with a mean of 60, and a range of 20.
B: The number of coins in this box was drawn from an unknown probability distribution. Our best estimate of the number of coins in this box is 60, based on certain information that we have available. We are certain that the actual value is within 20 gold coins of this.
With regards to understanding the example, and understanding how to apply the kind of Bayesian reasoning that the article recommends, it’s important to understand that the example was based on B. And in real life, B describes situations that we’re far more likely to encounter.
With regards to understanding human psychology, human biases, and why this feels like a paradox, it’s important to understand that we instinctively tend towards “A”. I don’t know if all humans would tend to think in terms of A rather than B, but I suspect the bias applies widely amongst people who’ve studied any kind of formal probability. “A” is much closer to the kind of questions that would be set as exercises in a probability class.
I think there’s some value in that observation that “the all 45 thing makes it feel like a trick”. I believe that’s a big part of why this feels like a paradox.
If you have a box with the numbers “60” and “20″ as described above, then I can see two main ways that you could interpret the numbers:
A: The number of coins in this box was drawn from a probability distribution with a mean of 60, and a range of 20.
B: The number of coins in this box was drawn from an unknown probability distribution. Our best estimate of the number of coins in this box is 60, based on certain information that we have available. We are certain that the actual value is within 20 gold coins of this.
With regards to understanding the example, and understanding how to apply the kind of Bayesian reasoning that the article recommends, it’s important to understand that the example was based on B. And in real life, B describes situations that we’re far more likely to encounter.
With regards to understanding human psychology, human biases, and why this feels like a paradox, it’s important to understand that we instinctively tend towards “A”. I don’t know if all humans would tend to think in terms of A rather than B, but I suspect the bias applies widely amongst people who’ve studied any kind of formal probability. “A” is much closer to the kind of questions that would be set as exercises in a probability class.