What is 2.2204460492503E-16 as odds?

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Discussion Overview

The discussion revolves around interpreting the number 2.2204460492503E-16 in terms of odds, exploring its mathematical implications and the context of its precision. Participants engage in calculations and clarifications regarding probability and odds, with references to specific scenarios such as coin flips.

Discussion Character

  • Mathematical reasoning, Technical explanation, Debate/contested

Main Points Raised

  • Some participants estimate the odds represented by 2.2204460492503E-16 to be around 1 to 100-trillion or possibly 1-quadrillion.
  • One participant provides a mathematical breakdown of the number, relating it to femto and atto units, and notes that terminology may vary by location.
  • There are questions regarding the origin of the number and its precision, with one participant expressing skepticism about how such a precise measurement was obtained.
  • Another participant states that 2.2204460492503E-16 is equivalent to (0.5)^52, suggesting that the odds of getting heads 52 times in a row could be approximately one to one-quadrillion.
  • A clarification is made regarding the distinction between odds and probability, with a participant explaining how to calculate odds from probability.
  • One participant asserts that the odds of getting heads 52 times in a row is indeed one in 4.5 quadrillion.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the number and its implications for odds, with some calculations leading to varying estimates. The discussion remains unresolved regarding the exact interpretation and implications of the number.

Contextual Notes

There are limitations regarding the assumptions made about the number's origin and the definitions of terms like femto and atto, which may vary by region.

bsharvy
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TL;DR
How to convert really small numbers to odds format
I think it's around 1 to 100-trillion, but maybe 1-quadrillion?
 
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##
\begin{align*}
2.2204460492503E-16&=2.2204460492503\cdot 10^{-16}\\
&\approx 0.222\cdot 10^{-15} =0.222 \text{ femto (f)} \\
&= 222 \cdot 10^{-18} \text{ atto (a)}
\end{align*}
##
Whether you call femto a billiardth or a quadrillionth and atto a trillionth or a quintrillionth depends on your location on earth.
 
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bsharvy said:
2.2204460492503E-16
Did you just make this number up? How did you make this measurement to this precision?
 
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berkeman said:
Did you just make this number up? How did you make this measurement to this precision?
It is (0.5)^52

So, are the odds of getting heads 52 times in a row approximately one to one-quadrillion?
 
Last edited by a moderator:
Let p be the probability of an event.
Then 1-p is the probability of the event not happening.
So the odds are 1-p to p.
You can divide by p to get ##\frac 1 p -1 ~to~1##
 
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bsharvy said:
the odds
You mean "the probability"
 
bsharvy said:
It is (0.5)^52

So, are the odds of getting heads 52 times in a row approximately one to one-quadrillion?
Yes. One in 4.5 quadrillion.
 

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