At some point in your life you must have been torn between two choices on a math exam. When this question first came up Although the answer is said to be 1/2 It was later put forward that the answer was 1/3. This ‘non-answer’ still continues. In other words, choosing between more than one answer on exams does not always lead to errors.

Looking at the question, maybe you too For the answer you will be divided in two. For this reason, it is worth noting that we cannot provide you with the correct answer from the start. Now let’s move on to the question.

There will be a ‘Sleeping Beauty’ in this problem, which appears as the Sleeping Beauty Problem.

This problem has brought mathematicians into conflict with each other due to different results. What’s more interesting is that there are more than 100 studies on this topic. It does not tell us which solution of these studies is the correct one.

Basically one probabilistic problemActually, it’s just a thought experiment. To clarify this issue, researchers decided to try this experiment on a person. The reason why the experiment is called Sleeping Beauty has to do with the way the subject is put to sleep and wakes up.

As part of the experiment, the sleeping person is given a sleeping pill on Sunday and helped to fall asleep.

The subject who has prior knowledge about the experiment is put to sleep. Those conducting the research flip a coin and if it stands out, it’s heads; On Monday they wake up the sleeping person. And they ask this person about the probability that the coin will land on heads. However, if they get a tail, they will wake this person up on Monday.

They then give this person another sleeping pill to help him sleep again. They ask the question again to this person who was woken up again on Tuesday. Thus ends the experiment. The person sleeping during this process under the influence of sleeping pills It cannot distinguish whether it has awakened before or not.

Put yourself in this person’s shoes: You know that you are being subjected to such an experiment and that you will be asked some questions during the experiment.

But when you wake up, you don’t know what day it is or whether you’ve woken up before.. The intuitive answer will usually be 1/2. Because the chance of heads when tossing a coin is always 1/2.

When the sleeping person wakes up, He cannot know whether it is Monday or Tuesday; but the condition of the coin has no bearing on this fact. No matter what day he wakes up, the result will always be the same.

When we think about this problem, three different scenarios emerge. He will be woken up in the same way on Monday when heads start to rise When the text message arrives on Monday, he will be woken up again. and he will be awakened when the letter arrives on Tuesday.

So, what are the odds for each event?

According to the calculation of conditional probabilities, all three situations are equal. philosopher of science Adam Elga We want to explain it with the formula: Let today be Monday (M). P stands for probability.

Monday/Head (M, T) and Monday/Tail (M, Y) The probabilities for the states are demonstrably equal: P (M, T) = P (M, Y) = 1/2. Likewise, if the sleeper wakes up and discovers that tails have arrived, that day must be Monday or Tuesday. In this case too P(M,Y) = P(T,Y) = 1/2. Combining these equations, thanks to the transition property we obtain the triple equality P (M, Y) = P(M, T) = P(T, Y). Given that the total probabilities are 1, each value is 1/3.

You’re confused we know. Don’t worry, we had trouble figuring it out too.

Your thoughts about the result, which you initially thought was 1/2, may have changed, you may have some doubts.

Those who say the answer is 1/2 are based on the number of experiments, while those who say 1/3 are based on the number of times the sleeping person wakes up. While proponents of 1/2 approach it from the experimenter’s perspective The ones defending 1/3 are from the sleeping person’s perspective. make calculations. Mathematics does not always provide objective answers. The answer you give may be related to your feelings and prejudices.

The result is that even though the problem seems to have only one solution, it surprises everyone that it has two consequences. has become a problem in case of. So where did you find the answer to?

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