Probability · experts disagree
The Sleeping Beauty problem
Circulated by Arnold Zuboff in the 1980s; put into print by Adam Elga in 2000, with David Lewis replying in 2001.
On Sunday, Beauty agrees to an experiment and is told every detail of it. She will be put to sleep. A fair coin will be tossed. If it lands heads, she will be woken on Monday, interviewed, and sent home. If it lands tails, she will be woken on Monday, interviewed, put back to sleep with a drug that wipes her memory of that waking, then woken again on Tuesday and interviewed again. The two interviews are identical, and she cannot tell which day it is.
She wakes. Before anyone tells her anything, the interviewer asks: 'What is your degree of belief that the coin landed heads?' She knows the whole setup and reasons perfectly. What should she answer?