alarm clock

You are the subject of an experiment in which the protocol is as follows. On Sunday evening, we were asleep and you start a coin not rigged. If the coin falls on FACE, the next day (Monday) we wake up and we have an interview with you. If so BATTERY, it wakes you up, there was an interview with you, and you sleep again submitting to a treatment that causes total amnesia of the day Monday, Tuesday, and finally, it wakes you up again and we have an interview with you. In interviews, they ask you "what you assign probabilities and FACE PILE for the coin toss Sunday (which remained in place hidden under a box)? ". Two arguments seem possible.  
First argument: "I am sure that the room is normal. I have no information in addition to that I had on Sunday night before falling asleep. Before falling asleep, the probability is 1/2 for each event or FACE PILE. So when I woke up during the experiment, I have to assign probability 1/2 to each contingency. "
Second argument: "Suppose we do the experiment 100 times by operating 100 weeks on. In about half weeks (50), I awake on Monday after a FACE draw. Other weeks (about 50) BATTERY has been shot and I awake on Monday and Tuesday (so there will be about 100 clocks). In total, during the 100 weeks, I awake about 150 times and of these 150 clocks, FACE will be 50 times the right answer and the right answer will BATTERY 100 times. Whenever I woke up, the probability that the piece is launched on Sunday fell on FACE is 1/3, and 2/3 is BATTERY. My answer is: FACE 1/3 and 2/3 BATTERY! "

Answers : 

This paradox (called "paradox of Sleeping Beauty") seems to have found a permanent solution and supporters of both options exchange their arguments today but failed to agree (look for "sleeping beauty paradox" on Internet). However, my preference is clearly to the second solution because of the following argument. While the second argument seems in any acceptable point, the first argument could be defective and therefore not sufficient to conclude 1/2 to 1/2 Battery for Face. Indeed, to assess a probability or, more generally, to know the numerical value of a parameter that is measured, it must take into account the changes or distortions of the greatness that is measured. If, for example, you measure the size of a postage stamp with a double decimeter placed above a magnifying glass covering the stamp, the value you will find exaggerated compared with reality; we speak of "magnifying effect". You will find 2 cm while the stamp actually measures 1 cm. Another example of deformation, if you want to measure "the proportion of fish that are smaller than 50 cm" in a lake, fishing a 100 fish sample with a net with a mesh size of 20 cm, you will find a value well below the reality because your net lets all fish less than 20 cm. There is talk of a "filter effect". Here, when you submit the experimental protocol, you measure the likelihood of battery and Face by examining the room on Sunday before it is launched and you find half for Battery, 1/2 to Face. It is then the property of the room (with regard to the draw on Sunday evening) is subjected to a kind of double-magnifying effect that your Piles of observations (since when battery is pulled, you watch Monday and Tuesday), whereas this is not the case when the face is drawn. As in the case of the magnifying glass - that is to say, for those who observe the stamp through a magnifying glass - the observed probability and measured by you is 2/3 and 1/3 Battery for Face, although actually - for those who do not look through the magnifying glass, that is to say, for one who is not caught in the experimental protocol - the probability is 1/2 to 1/2 for battery and Face. In conclusion: if you accept my way of thinking, when you wake up you have to answer for Face 2/3, 1/3 for battery because you are in the protocol and therefore subject to a magnifying glass effect. But this does not, of course, if they were subjected to a test piece, the piece would give 50% of cells and 50% Faces. The second argument is good while the first confuses what is measured "on the magnifying glass" with the object under the microscope.