 .
It is then easy to verify that OE entails
 .
So when Beauty wakes up on Monday morning (and of course likewise if and when she wakes up on Tuesday) she should think that the probability of Heads is 2/5. The reason, in intuitive terms, why the probability is less than 1/2 is that a smaller fraction of all observer-moments in her reference class would have her evidence if Heads (namely, 1 out of 3 observer-moments) than if Tails (2 out of 4 observer-moments).
If instead Beauty puts only subjectively indistinguishable observer-moments in her reference class,
 ,
then one can easily see that the observer-moments who have just woken up but haven’t been told what day it is (i.e.  ,  , and  – or “ ” for short) should all assign a 1/2 credence to Heads. For in this case, all observer-moments in their reference class, which was guaranteed to be non-empty, would have the evidence e2 independently of how the coin fell.
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