/sci/ - Science & Math » Thread #11503784

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Anonymous Thu 26 Mar 16:59:56 2020 No.11503784 View Reply Original Report

Quoted By: >>11503796 >>11503804 >>11503833 >>11503839 >>11503895 >>11504585 >>11504606 >>11505678

How do I calculate the probability that something is a fair coin or not a fair coin.

I have flipped the coin 74 times

32 heads
42 tails.

I just want to know the odds that the coin is actually in reality fair.

Pic unrelated

Thanks

Anonymous

Anonymous Thu 26 Mar 2020 17:05:30 No.11503796 Report

Quoted By: >>11503830

>>11503784
50/50 either it is or it isn’t

Anonymous

Anonymous Thu 26 Mar 2020 17:10:30 No.11503804 Report

Quoted By: >>11503830 >>11505705

>>11503784
By Bayes theorem:
P(coin is fair |32 heads, 42 tails) = P(coin is fair) * P(32 heads, 42 tails | coin is fair) / (P(coin is not fair) * P(32 heads, 42 tails | coin is not fair) + P(coin is fair) * P(32 heads, 42 tails | coin is fair)).

It's obvious that
P(32 heads, 42 tails | coin is fair) = (74 choose 32) * (1/2)^74.
P(32 heads, 42 tails | coin is not fair) = 1
P(coin is fair) = 0
P(coin is not fair) = 1

Plug those numbers in the equation above to get

P(coin is fair |32 heads, 42 tails) = 0
So the coin is almost surely not fair given those results.

Anonymous

Anonymous Thu 26 Mar 2020 17:29:23 No.11503830 Report

Quoted By:

>>11503796
Lol.
>>11503804
I'm sure the stats are reasonable, but that doesn't seem sensible to me.... Surely it's hasty declaring a coin as unfair with a discrepancy of 10 and only 74 flips?

Anonymous

Anonymous Thu 26 Mar 2020 17:31:26 No.11503833 Report

Quoted By:

>>11503784
fuck off redditor

Anonymous

Anonymous Thu 26 Mar 2020 17:34:26 No.11503839 Report

Quoted By: >>11503842

>>11503784
For a binomial distribution with p = 1/2 and n = 74, 1 - P(32<X<42) ~= 29.54%

Anonymous

Anonymous Thu 26 Mar 2020 17:37:03 No.11503842 Report

Quoted By: >>11503882

>>11503839
so theres a 30% chance that the coin is fair?

Anonymous

Anonymous Thu 26 Mar 2020 17:51:35 No.11503882 Report

Quoted By: >>11503889

>>11503842
No, assuming the coin is fair, there is a ~30% chance of getting your outcome.

Anonymous

Anonymous Thu 26 Mar 2020 17:54:38 No.11503889 Report

Quoted By: >>11504086

>>11503882
ok cool thanks.

Im assuming the odds that i get 37 heads and 37 tails is 50%?

Anonymous

Anonymous Thu 26 Mar 2020 17:56:22 No.11503895 Report

Quoted By:

>>11503784
n=74
k=32 or 42
https://en.wikipedia.org/wiki/Binomial_distribution#Probability_mass_function

Anonymous

Anonymous Thu 26 Mar 2020 19:38:00 No.11504086 Report

Quoted By:

>>11503889
Important point: If you define a fair coin as a coin with exactly 50% of each outcome, given enough trials, it's inevitable that you'll find the hypothesis that it's not to be much more likely. A better mathematical translation of the idea would be to use an interval instead of a point hypothesis, such as defining fair as between 49% and 51% odds.

Anonymous

Anonymous Thu 26 Mar 2020 22:37:57 No.11504585 Report

Quoted By:

>>11503784
Always go for the tails.
The head tends to be heavier most of the time and would likely be at the bottom

Anonymous

Anonymous Thu 26 Mar 2020 22:44:34 No.11504606 Report

Quoted By:

>>11503784
The probability is either 100% or 0% that it is fair. There is no method to calculate which of them it is. But statistics defines a notion of "confidence". If the coin tends to land on equal amounts of heads and tails, then you grow increasingly confident that the coin is fair, as you make increasing number of flips.

Anonymous

Anonymous Thu 26 Mar 2020 23:11:49 No.11504672 Report

Quoted By: >>11504685

does anyone itt apply this stuff to finance?

Anonymous

Anonymous Thu 26 Mar 2020 23:15:27 No.11504685 Report

Quoted By: >>11504697

>>11504672
What stuff? You mean statistics?

Anonymous

Anonymous Thu 26 Mar 2020 23:20:05 No.11504697 Report

Quoted By: >>11504755

>>11504685
probability

Anonymous

Anonymous Thu 26 Mar 2020 23:50:47 No.11504755 Report

Quoted By:

>>11504697
You want to apply probability, without using statistics? Have you got some idea how that will work exactly?

Anonymous

Anonymous Fri 27 Mar 2020 06:53:33 No.11505678 Report

Quoted By:

>>11503784
It depends what percentage of coins are fair. You can't get a probability for this without that, but if you assumed 50% you could get a very rough estimate for cases where it isn't something crazy big or small.

Anonymous

Anonymous Fri 27 Mar 2020 07:06:51 No.11505705 Report

Quoted By:

>>11503804
Is this what /sci/ has come to? Are people on this board really this fucking retarded now?

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