That’s an interesting conjecture, and I wonder if you have any evidence for it. In teaching probability and asking students this exact question about the result

That’s an interesting conjecture, and I wonder if you have any evidence for it. In teaching probability and asking students this exact question about the results of coin tosses, most do say the second sequence is more likely (early in the class), and they are in fact answering the question that we intend them to answer. But, after further discussion, most accept that the sequences are equally likely. It’s my observation of that specific transition in understanding that convinces me that they are, in fact, considering the particular sequences that we want them to consider, and not, as you conjecture, substituting a general notion of some class of sequences. Further, there are always those several students who just never buy it, no matter how much evidence and calculation I show them. They can’t overcome their faulty intuitions.