Conflict between experimental and theoretical probability results

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Discussion Overview

The discussion revolves around the conflict between experimental and theoretical probability results, specifically in the context of coin tossing experiments. Participants explore the discrepancies observed in the number of heads versus tails across multiple experiments and question the implications of these results on the understanding of probability.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that theoretical probability suggests a 50/50 chance for heads and tails, yet experimental results show a consistent occurrence of more heads than tails.
  • One participant suggests that the observed bias could be due to the coins being used, implying that they may not be perfectly fair.
  • Another participant mentions that as the number of trials increases, the results should converge towards 0.5, yet they found documentation of a rare case where tails outnumbered heads after several trials.
  • There is a suggestion that the assumption of no bias in coin flipping experiments may not hold true in practice.
  • Some participants express skepticism about the validity of the experimental results, questioning whether all experiments consistently showed heads leading tails.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the observed bias in the results is due to the coins themselves or if it is merely coincidental. Multiple competing views regarding the nature of the bias and its implications for probability remain present.

Contextual Notes

Participants highlight the limitations of the experiments, including the potential for bias in the coins used and the small sample sizes in some cases. There is also an acknowledgment that the assumption of fairness in coin tossing may not be universally applicable.

Who May Find This Useful

This discussion may be of interest to those studying probability theory, experimental design, or anyone curious about the practical implications of theoretical concepts in probability.

Akshay_Anti
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Hello!

Recently, I read abt some experiments related to probability which involved tossing of coins.It listed the experiments performed by following-
Comte buffon:- 2048 heads from 4040 tosses.
J E Kerrich:-5067 heads from 10000 tosses.
Karl Pearson:-12012 heads from 24000 tosses.

My question- Theoretical probability states the result should be approximately 0.500. Okay, agreed! But why only number of heads is greater than number of tails and not vice versa?

Thanks in advance
 
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It may happen accidentally, or the coin used may be biased. But notice that for the last experiment the bias is very low. In the limit, we expect the result be 0.5 as you agreed.
 
exactly... as the no of trials increase, the value tends to 0.500

but when i searched for documentations on net, i found only 1 case when no of occurences of tails was larger.. And that too after 15 cases in favour of heads... Any idea why?
 
Then I think there may be a little bias as both sides of a coin are not completely the same.

Notice that in probability, the experiment "flipping a coin" assumes that there is no bias.
 
Last edited:
true that... but all coins being biased in a similar fashion that heads turn up more than tails? That's not just co-incidence...
 
Akshay_Anti said:
true that... but all coins being biased in a similar fashion that heads turn up more than tails? That's not just co-incidence...

1/ None of the coins are biased.
2/ That's just co-incidence.

These four figures indicate nothing. Are you sure that at all stages the of all those four experiments Heads were ahead of tails?
 

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