d) That one person believed that choice B was to be taken literally. That is, that B really (really!) means that the very first coin flip came out tails—NOT HEADS! - tails, the second heads, the third tails, and so on.
I’m sorry—I suppose I’m probably missing something, but I can’t think of any other possible way to interpret this question. I agree that it is far more probable to see a sequence equally containing both heads and tails than one containing only heads, but it seems like you are asking for the relative probabilities of two highly specific sequences of the same length. Could someone please explain?
Longitudinal studies can and should include control groups. The difference with RCTs is that the control group is not randomized. Instead, you select from a population which is as similar as possible to the treatment group, so an example is a group of people who were interested but couldn’t attend because of scheduling conflicts. There is also the option of a placebo substitute like sending them generic self-help tips.
ETA: “Longitudinal” is also ambiguous here. It means that data were collected over time, and could mean one of several study types (RCTs are also longitudinal, by some definitions). I think you want to call this a cohort study, except without controls this is more like two different cross-sectional studies from the same population.