Quote by ParticleGrl
Everyone agrees the dice would roll both sequences with equal probability. Thats not the question being addressed in the second example.
The question being addressed in the second example is 'presented with two numbers, one of which was generated by rolling dice, one of which was generated with a different unknown process, which was more likely to be generated by the dice?'
In this case, I think many approaches will suggest the string of 1s is less likely to be the dice, but with only one data point and no information about the process generating the nondice number, the predicted probabilities will always be close to 1/2 for each.

I don't understand how that question is the question that arose in the second part.
Here is what is being said:
"But let’s say you tossed a die out of my view and then said that the results were one of the above. Which series is more likely to be the one you threw? Because the roll has already occurred, the answer is (b). It’s far more likely that the roll produced a mixed bunch of numbers than a series of 1’s."
This does not relate to the first statement. The roll sequence is more likely to produce a string of mixed numbers. However, what we have here is a choice between two specific strings of numbers. Her conclusion, "thus, the answer is (b)" is false. Everything else that she said is technically fine, but largely irrelevant. The probability that the sequence is a mixed sequence of numbers is not the same thing as the probability that the sequence is a PARTICULAR mixed sequence of numbers.