The best answers are voted up and rise to the top Unfortunately I dont have by now the knowledge to make an answer. Probabilities can't really be derived from experience alone, you need to start with some sort of "inductive bias" in order to draw conclusions from evidence.The heuristic approach of hypothesis testing gives a framework for making decisions in these situations, but it doesn't pretend to assign probabilities to those hypotheses.In particular, we note that if $r$ is the actual probability that the coin will land on "heads" rather than "tails", then if we got $h$ heads and $t$ tails, the distribution of $r$ is described by the probability density function Random Number Generator Repetition, unique, sort order and format options. However, sometimes even after hundreds of years, some new results might come up which disprove it. In a world (more like the real world) where no coin is truly fair, then there is automatically a 100% chance that your coin is unfair. For $20$ straight heads, we compute After the coin has been caught or landed, the parties involved in the game are required to look at which side has the coin landed on. The next instance of 1000 flips can use a different coin. By using our site, you acknowledge that you have read and understand our Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. This form allows you to flip virtual coins.

However, in this case, $k=n$ because we are calculating what happens when all the flips are heads, so there is only one term in the sum. For $k=50$ the probability is less than $1$ in a quadrillion.

Not one specific coin mind you, but all instances ever, anywhere, of flipping one coin 1000 times.

To me the uses of law of larger numbers is fundamental here or some analysis at the level of variance more than mean. How to solve that other ways?

In your case, the probability of your event, 1000 heads, or something at least as strange, is $2\times1/2^{1000}$ (that is because you also count 1000 tails).Now, with statistics, you can never say anything for sure.

Yikes! And because these two sides are in some sort of a conflict or disagreement, the game of flipping the coin will help them in resolving that conflict and reaching an agreement. If you flip three coins, it's eight - two for the first times two for the second times two for the third. By your logic, the probability of this outcome is $1$ in a quadrillion, so it's practically impossible that it happened by chance. If a coin was observed to give a set of flips that was THTHTH..., I would use the binomial distribution and get about 11%, and conclude that the this is not unlikely enough to discard the hypothesis that the coin is fair. Decide-o-matic; Daily Horoscope; 10 Tips for Making Effective Decisions; Games. If you'd like to model with something in between, say 50% of coins are truly fair, and the other 50% is distributed some way among $p\in[0,0.5)\cup(0.5,1]$, then based on that information we could calculate a more interesting answer.This is an issue not so much about mathematics as about the real-world background to the coin-tossing experiment. So, we might conclude that we have a "magic coin".

The two sides can contain groups of people or even just individual people, but they must be competing groups or individuals. There are many online flip coin generators that can be accessed on a mobile phone, laptop, computer or tablets with a simple internet connection. Subscribe for more.

Is flipping a coin 50/50? $$ We have a better option to select fliping timing within 1 click.Google has made this game initially to entertain its users, but we have added more value into it and we are dedicated.

This is an old website to provide you game with little variation. Learn more about Stack Overflow the company Anybody can answer Now, let's say that the coin is "fair" if $r$ (which should be exactly $1/2$) falls between $0.45$ and $0.55$. P = \int_{.45}^{.55}f(r\mid T=t; H=h)\,dr = It is usually that there be two sides with opposing aims and views. \end{align}$P(U \mid{H})$ : probability of the coin being unfair conditioned to getting 1000 heads Some elements of that sample space would have 1000 heads. The total number of possible outcomes of flipping a coin 1000 times is 2^1000. The next instance of 1000 flips can use a different coin. For $k=7$ the probability is $1$ in $128$. If you assumed a specific distribution for the fairness of all coins, then we'd have the necessary information to calculate an answer for your literal question. which is very small. r^h(1-r)^t Convincing fake coins are fairly common: for example, about 5% of the £1 coins circulating in the UK are counterfeit*.

If the user is playing this game on their phone or tablet, they can simply touch the relevant button.

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