The Sleeping Beauty Problem


The Paradox goes around the well-known fairy-tale princess participating in an experiment. The experiment commences on a Sunday. The princess is told that she will be put to sleep and the experiment will proceed on the toss of a fair coin. If the coin comes up heads, she will be awakened on Monday, interviewed and put back to sleep. However, the princess will have no recollection of the interview or being woken up. If the coin turns up tails, the princess will be woken up on Monday and Tuesday, will be interviewed and be put back to sleep with zero recollection. In either case, the experiment ends on waking up the princess on Wednesday without the interview aspect. 

Whenever Sleeping Beauty is awakened and interviewed, she will not be aware of the day or whether she has been awakened before. During each awakening, she is questioned- “What is your degree of certainty* that the coin landed heads?” 

Upon basic analysis we figured out that since the Princess will have absolutely zero recollection of the experiment, there is no way to arrive at the solution other than basic probability. In simpler words, the probability of heads showing up on tossing an unbiased coin. The answer is half. 

                                                        

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