See also: Probability is in the Mind, You Are Never Entitled to Your Opinion, and “I don’t know.”Naive Bayes is a reader-supported publication. To receive new posts and support my work, consider becoming a free or paid suscriber. I. Suppose you have a random number generator, which gives values from 1 to 6. Like a die, but not necessarily a literal one. Let’s call it a “die” anyway. You don’t have any other information about the relative frequency of the outcomes, and have no reason to expect one outcome more than any other.
It's not really true that "more information is given in the second question". Maybe explicitly. But we all assume a fair die in the first question (you do even say "random number generator"). So the "additional" information in the second question is really just different information.
If you limited the first prompt to saying that the mean is 3.5, more people would have the same reaction to both questions, i.e. there are multiple ways to achieve a mean of 3.5 or 4.5.
It's not really true that "more information is given in the second question". Maybe explicitly. But we all assume a fair die in the first question (you do even say "random number generator"). So the "additional" information in the second question is really just different information.
If you limited the first prompt to saying that the mean is 3.5, more people would have the same reaction to both questions, i.e. there are multiple ways to achieve a mean of 3.5 or 4.5.