What is the Sleeping Beauty problem?

The Sleeping Beauty problem is a philosophical puzzle that involves probability and self-locating belief. Here's how it's structured:

• Setup: Sleeping Beauty is put to sleep on Sunday. A coin is flipped, and if it lands heads, she is awakened on Monday and then put back to sleep with her memory erased. If it lands tails, she is awakened on both Monday and Tuesday, with her memory erased each time she is put back to sleep.

• Question: When Sleeping Beauty is awakened, she does not know which day it is. She is asked to assign a probability to the event that the coin landed heads.

This leads to two primary schools of thought:

1. The "1/2" Argument: One might intuitively think that since the coin flip is fair, the probability of heads is simply 1/2.
2. The "1/3" Argument: Others argue that since there are twice as many waking periods if the coin lands tails, the probability of the coin landing heads should be considered 1/3 1.

This problem is connected to concepts in probability theory and decision-making under uncertainty. It's often used to illustrate questions about how to update beliefs when new, self-locating information is obtained.