Science and myths's video: paradox sleeping beauty paradox

On Sunday, Sleeping Beauty agrees to participate in an interesting experiment, run by a professor. She gets a sleeping pill and goes to sleep. The professor then tosses a fair coin. From now on, there are two possibilities: the coin comes up heads. In this case, the professor will awake Sleeping Beauty on Monday and ask her: “What is the probability that the coin came up heads?” After this, the experiment ends. the coin comes up tails, in which case Sleeping Beauty is also awakened on Monday, asked the same question, but put to sleep again and awakened on Tuesday, to once again be asked the same question. Note that the sleeping pill also causes Sleeping Beauty to forget any earlier awakening: her memory is the exact same whether she awakes on Monday or on Tuesday. Sleeping Beauty awakens. She knows about the structure of the experiment, but naturally doesn’t know whether it is Monday or Tuesday. The professor asks: “What is the probability that the coin came up heads?” A fair coin has a 1/2 probability of coming up heads. Sleeping Beauty doesn’t know what day it is when she wakes up (it’s either Monday or Tuesday), but the coin didn’t care about this fact; it’s a fair coin no matter what day Sleeping Beauty wakes up. It may thus seem logical for Sleeping Beauty to answer “1/2” when the professor asks: “What is the probability that the coin came up heads?” But imagine we run this whole experiment 6 million times. The results will look roughly as follows: That is, Sleeping Beauty will wake up twice as much after tails as after heads. Let’s say she earns $1 if she correctly guesses the coin flip result. She’d make twice as much money if she always guesses “tails” in the above experiment as she would if she always guesses “heads”. That suggests that, when Sleeping Beauty wakes up, she should answer 2/3 probability to “tails” and 1/3 to “heads”. But what about what we said earlier — that the day Sleeping Beauty wakes up can’t possibly influence the fairness of the coin, and that therefore her answer should be “1/2”? There’s a distinction to be made. The coin really is fair, but that doesn’t mean Sleeping Beauty should estimate a 1/2 probability after the coin flip. Is waking up somehow evidence that the coin came up tails? Yes! In the above 2 million run experiment, Sleeping Beauty wakes up a total of 3 million times, 2 million of which are on a Monday. Upon waking up, she should therefore estimate the probability of “it’s Monday” on 2/3. 1 million Monday runs came after heads, so given that it’s Monday, the probability of heads should be estimated at 1/2. If it’s Tuesday, this probability is 0: only after tails does Sleeping Beauty wake up on Tuesday. The overall probability of heads can then be calculated as 2/3 * 1/2 + 1/3 * 0 = 1/3. Or, we could simply note that in the table, we can see 1 million heads runs. Dividing that by the total of 3 million runs gives a 1/3 probability. Waking up is evidence for tails because it’s possible that it’s Tuesday, in which case it’s definitely tails. It could also be Monday, but that doesn’t “favor” heads: Monday gives equal probabilities to both heads and tails. To know more watch out this full video till the end . Thanks for watching ! Social accounts link Instagram- https://www.instagram.com/scienceandmyths/ Facebook Page- https://www.facebook.com/ScienceAndMyths/ FAIR-USE COPYRIGHT DISCLAIMER This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.