But we don’t know what the probability of a Tuesday tails outcome is.It could be zero it could  be one-third it could be something else entirely.So what do you think?

Do not hit the like or dislike button yet! I want you to consider a problem that’s been one of the most controversial in math and philosophy over the past 20 years, with no consensus answer. Listen to the problem and then vote for the answer you prefer using the like and dislike buttons.

Here is the setup: Sleeping Beauty volunteers to be the subject of an experiment. Before it starts, she’s informed of the procedure. On Sunday night she will be put to sleep. A fair coin will be flipped. If it comes up heads, she’ll be awakened on Monday and then put back to sleep. If the coin comes up tails, she’ll be awakened on Monday and put back to sleep, and then awakened on Tuesday and put back to sleep. Each time she gets put back to sleep, she will forget that she was ever awakened. In the brief period anytime she’s awake, she will be told no information. But she’ll be asked one question: What do you believe is the probability that the coin came up heads?

So how should she answer? The intuitive answer that pops into my head is clearly one in three. It could be the Monday when it came up heads. Or it could be the Monday when it came up tails. Or it could be the Tuesday when it came up tails.

The simple reason why Sleeping Beauty should say the probability of heads is one half is because she knows the coin is fair. Nothing changes between when the coin is flipped and when she wakes up, and she knew for a fact that she would be woken up and she receives no new information when that happens.

Others would argue that something does change when she’s awakened. She actually learns something important: she learns that she’s gone from existing in a reality where there are two possible states (heads or tails) to existing in a reality where there are three possible states (Monday heads, Monday tails or Tuesday tails). Therefore she should assign equal probability to each of these three outcomes, where heads only occurred in one. So the probability that the coin came up heads is one-third. This is known as the thirder position.

What do you think? The chance of waking up on Monday with heads is 50 percent and the chance of waking up on Monday or Tuesday with tails should be 50 percent. Therefore, the tails probability gets split across two days, 25 percent each. However, if you repeat the experiment over and over, you find that Sleeping Beauty wakes up a third of the time Monday heads, a third of the time Monday tails, and a third of the time Tuesday tails, not 50-25-25 like the previous analysis would suggest.

If you were Sleeping Beauty and were asked “What’s the probability the coin came up heads?”, the answer may seem obvious to some, but to others the other answer seems equally obvious. This has led to hundreds of philosophy papers being published on this problem over the past 22 years.

Another thought experiment is if Brazil plays Canada five times and the experiment is done each time. If you say Brazil each time you’re woken up, you’ll probably be right about four out of five of the games. However, if you said Canada every time you would be wrong about those four games but right 30 times in a row when you’re repeatedly asked about Canada’s one victory. If you stand to win a bet by correctly answering the question, then by all means you should bet on Canada. If you want to correctly pick the winner of more of the games, you should say Brazil. This is what’s at the heart of the dispute between Halfers and Thirders in the Sleeping Beauty problem. If you want to be right about the outcome of the coin tosses, you should say the probability of heads is a half, but if you want to answer more questions correctly, you should say one-third.

Imagine that you know for a fact that before our universe began, there was a coin flip and if it came up heads, only a single Universe would be created. But if it came up tails, a quasi-infinite Multiverse would be created and in each of those Multiverse universes, you’d find every possible variation of Earth and the people on it. In some versions, there would be no Earth.

Now you becoming conscious is just like Sleeping Beauty waking up. There’s no way to tell if you’re in that single universe or in one of the Multiverse universes, but you know there are a lot more of them. So would you think that you’re for sure in the Multiverse, or are the chances 50/50?

The best way to develop intuition about probability is by working through scenarios or running simulations like we did for Sleeping Beauty. This video’s sponsor, Brilliant, offers probability courses that walk you through lots of situational probability questions. You can try it free for 30 days at brilliant.org/veritasium. Brilliant is the best way to learn because it forces you to think critically and it’s also a lot of fun. With Brilliant, you can model the real world with math and expand your understanding of cutting edge topics like AI and machine learning - technology that’s transforming our world right now.

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