Law of large numbers | Probability and Statistics | Khan Academy

Introduction to the law of large numbers Watch the next lesson: https://www.khanacademy.org/math/probability/random-variables-topic/binomial_distribution/v/binomial-distribution?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Missed the previous lesson? https://www.khanacademy.org/math/probability/random-variables-topic/expected-value/v/expected-value-insurance?utm_source=YT&utm_medium=Desc&utm_campaign=ProbabilityandStatistics Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Probability and Statistics channel: https://www.youtube.com/channel/UCRXuOXLW3LcQLWvxbZiIZ0w?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Comments

1. so if flipping this coin a numerous amount of times after he is up at 70 doesn't guarantee that he gets tails more in the future, then why is there a guarantee that the average drops back down to 50% eventually??????
2. But why does he times 100 by 5 and get 50.He said Number trials to be times the probability of success of any trials .So is it 50 or 500 .
3. I am confused. Using same theory can't I say that it will not be equal to population mean ?
4. To put simply - Even if you carried out a routine 100 times where you flip a coin a fixed amount of times and found that it always landed on heads 70% if the time, you cant use that as concrete evidence to decide there is a 70% chance the coin will always land on heads. For example, it may land on heads 40% of the time if you repeated the routine another 100 times.
5. Bernoulli surely loved to shake his shoe boxes.
6. 1) if i flip the coin 100 times and i get all head, it doesnt mean that i get a tail in 101 flip because every flip is independent.
   2) the law of large number said if i go infinity flip, i will converge to the probability of 50% head. that mean tail will have more probability in the rest of the flip. but if i go infinity enough and still get head in every flip, that mean i can sure enough to get tail in the next flip, but they are still independent?
   3) isnt the probability of getting 50 head of 100 flip is 100C50 divide by 2^100 which is not 50%? even i approach infinity let say 1000C500 divide by 2^1000. it didnt seem to approach 50%.
   
   I just cant link all the concept together? can anyone help me pls.
7. Sal, you are a Hero. The world will remember you for centuries, for the work you've done. You will help milions of students with thse videos :D But you already know that :D I wanted just to say Ty, and Good job :D
8. so, the probability of getting a head or a tail will be equal to 50% only at infinity i.e. never??? Is it?
9. Great video sir. Very easy to understand.
10. good point. Thanks.
11. not very intuitive, not very precise, not good enouth
12. Is it fair to say that not knowing what the expected mean is, what the law of large numbers really tells us is that du/dn = 0 (with u the sample mean and n the number of trials) when the n tends to infinity? or in another words that the sample mean remains constant and that is what we call the expected mean
13. best explanation ever
14. You are awesome Khan
15. At 6:45, you said that the deviation from the expected value (more heads) is a low probability. What makes that so? Wouldn't this support the gambler's fallacy? Can a probability be calculated how many heads will occur (or not) after a series of consecutive flips that result in heads? 
16. Am i the only one here?...dude u were saying that since u had a lot of heads that doesnt mean that there are going to be tails...though u were drawing the average to fall..which means that u got more tails..
17. It all makes sense now
18. Thank You Khan Academy. My statistics professor is terrible.
19. Isn't the gambler's fallacy to say that since you won alot of times in the past you will continue to win
20. My father always says: "Chance has no memory" to describe the gambler's fallacy.