I mean in a purely abstract logical sense, a sample group of one has only a single outcome. It will either be 100% heads or 100% tails. Probability only has meaning in the wider context of multiple flips. True you don’t know ahead of time the outcome of a single flip, but it’s still definitely going to be all one outcome. Bayesian probability applies only to distributions of events. It says nothing about a single event. It says that in a sample group of infinite coin tosses, the distribution of heads and tails will be 50/50, and so all finite sample group distributions of two tosses or more approaches that ratio. But a single toss has no distribution, it simply is whatever outcome it is. So it’s not exactly accurate to say one event has an outcome of a certain probability unless you mean compared to a wider sample group. More directly stated, a sample group of one has no ratio of outcomes.
Exactly! But that’s not how the thought experiment used to illustrate the fallacy is traditionally presented. It’s asking for the probability of her outcome, not her and her fellow tellers and/or feminists. As I said before, the fallacy is quite real, but the way the example is perpetuates a common misunderstanding about what a probability actually is. I admit, it’s a minor point, but that was the one I was making.
