Understanding Probability and Fairness in Coin Tosses

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Discussion Overview

The discussion revolves around the concept of probability, particularly in the context of coin tosses. Participants explore how probability is determined, the implications of experimental data, and the nature of fairness in coin tossing. The scope includes theoretical aspects of probability, practical implications of experimental results, and statistical considerations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether probability is based on averages or small sets of experimental data, specifically in the context of flipping a coin 50 times and observing a disproportionate number of heads.
  • Another participant asserts that probability cannot be determined by measurements but can only be estimated through repeated independent experiments, suggesting that the observed frequency will approximate the true probability.
  • Some participants propose that if everything has an equal chance of happening, the probabilities can be adjusted based on constraints.
  • It is noted that if a coin is fair, the probability of landing on heads or tails is 50%, but a few tosses not yielding equal results does not necessarily indicate the coin is unfair. The complexity of determining fairness through sufficient tosses is highlighted.
  • References to external sources on Bayesian probability and statistical methods for checking coin fairness are provided for further exploration.

Areas of Agreement / Disagreement

Participants express differing views on how probability is determined and the implications of experimental results on perceived fairness. There is no consensus on the best approach to understanding these concepts.

Contextual Notes

The discussion includes limitations regarding the assumptions made about fairness, the dependence on the number of trials, and the complexity of statistical confidence levels in determining fairness.

gilishaky
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Hi, i was wondering if some one could explain to me some things about probability.

How is probability determined is it based on a average or a small set of experimental data? If you were to flip a coin Randomly 50 times and you get heads 40 times and tails 10 times could you then say you have a 80% probability to get heads then tails?

I know that having a 50% probability for example in a coin toss doesn't mean you'll get head or tails 50% of the time, you just have a chance to but then how do you infer how many times you will get head or tails.

Also if you flip a coin and have 50% probability to land on heads and you don't land on heads does that change the probability? or is it still 50%.
 
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gilishaky said:
How is probability determined

Probability can't be determined by any series of measurements. Probability theory says that if we conduct independent experiments where the probability of an event is some unknown but constant value then the fraction of times this event occurs in the experiments will probably be close to the probability of the event. In physics, people often refer to "physical probability" and assume that enough repeated experiments are guaranteed to approximate the probability of an event to an arbitrary precision.

Using data from experiments we "estimate" probability. We don't "determine" it.
 
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Assume that everything has an equal chance of happening. and based on constraints, adjust the chances of different events occurring accordingly.
 
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If your coin is fair and can't land on edge then by definition the probability of getting a head or tail is 50%.

If you make a few coin tosses and don't get an equal number it didn't automatically mean the coin isn't fair. The question how many times must you toss the coin to determine if it is fair is quite complicated. See...

https://en.m.wikipedia.org/wiki/Checking_whether_a_coin_is_fair

The field of statistics has quite a lot to say about confidence levels.
 

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