Turning to the case where there are outsiders (figure 13), we note first that their existence makes no difference unless they are included in the awakened Beauty’s reference class. If they are not included – if, for instance, Beauty’s reference class (at that time) is = – then her credence in Heads when wakening on Monday morning should simply be 1/2. “Outsiders”, however numerous, do not affect Beauty’s probabilities given this choice of reference class.
We can also note in passing that the assumption that the outsiders are not in (the reference class of ) implies that all know that they are in the experiment and consequently that they are not among the outsiders. For as we have argued earlier, every observer-moment’s reference class must include all other observer-moment that are subjectively indistinguishable from herself, i.e. all observer-moments who share the same total evidence that she has. So if the outsiders are not in then can infer that the outsiders have different evidence from their own, and thus that are not outsiders.
= 
– then her credence in Heads when wakening on Monday morning should simply be 1/2. “Outsiders”, 
) implies that