# Why is the sleeping beauty coin flip problem so complicated – its just flipping coins

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The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.

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Part of the problem is that you left out information about the problem. After they wake her they give her a drug to forget that she been awaken before so each time she wakes up she doesn’t know what day it is.

I’d advise looking up the problem on wikipedia

You’re missing half the text of the problem.

>Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
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>The important thing here is that because of the sleeping drug, Sleeping Beauty has no memory of whether she was woken up before. So when she wakes up, she cannot distinguish whether it is Monday or Tuesday. The experimenters do not tell Sleeping Beauty either the outcome of the coin toss nor the day.
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>They ask her one question after each time she awakens, however: What is the probability that the coin shows heads?

As other responses have mentioned you are missing half the question, the part where she doesn’t remember what happened previously when she is put to sleep and she is asked the probability the coin flip was heads. Also like many similar questions this isn’t really an issue of probability but instead revolves around precisely what is being asked. It is semantics, not mathematics.

In essence they have taken Sleeping Beauty and put her in a situation where she is being asked about an event with 50/50 chances (the coin flip), but engineered a situation where she answers more frequently when the coin lands on tails. If she guesses that the coin flip was heads then she would be wrong 2/3 times since she answers twice when it is tails!

This might be confusing, but only for people who are good at probabilities but have poor language skills. Sleeping Beauty is being asked:

> “What is the probability that the coin shows heads?”

She isn’t being asked what she thinks the coin flip was, so answering “50%” when the coin shows tails isn’t wrong. It is correct no matter what the coin flip turned out to be or how many times she is asked!

Now if she were asked something subtly different like “What is the probability you are awakening to a coin flip that landed heads?” then the answer of “1/3” makes sense.

[Veritasium did a pretty good video on this](https://www.youtube.com/watch?v=XeSu9fBJ2sI). The problem asks “If you’re Sleeping Beauty, *when they wake you up* what should you say is the probability the coin came up heads?”

– Some people say 1/2 because it’s a fair coin, end of story.
– Other people say 1/3 because you wake up twice in the Tails case and once in the Heads case. Basically *the fact that you’re awake* is evidence in favor of Tails, which should change your answer.