The Sleeping Beauty Problem

Sleeping Beauty agrees to an experiment. On Sunday she is put to sleep. A fair coin is flipped. If it lands heads, she is woken once on Monday, then put back to sleep with her memory of the waking erased. If it lands tails, she is woken on both Monday and Tuesday, with the memory of the Monday waking erased before Tuesday. Either way, when she wakes up she cannot tell which day it is or how many times she has already woken. When she is woken and asked "what is your credence that the coin landed heads?", what should she say?

The "halfer" answer says the coin is fair, she's learned nothing new about it upon waking, so the answer is 1/2. The "thirder" answer, now the more widely favored one, says she should reason about herself as a randomly selected waking-moment: there are three possible waking-moments in total (Monday-heads, Monday-tails, Tuesday-tails) and they are equally likely to be "this one," so heads is true in only one of the three, giving 1/3. The thirder camp treats her waking up as evidence, since tails produces twice as many wakings to be one of, which pulls her credence away from 1/2 in the same direction that seeing more heads-labelled tickets in a bag would.

There is no settled consensus among philosophers or statisticians on which answer is "correct," which is itself the reason interviewers like it: it tests whether a candidate can reason clearly about a genuinely contested foundation of probability rather than just recalling a memorized answer.