Difference between revisions of "K and k' values"
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Given a k'-value, {{M|k'\in\mathbb{N}_{\ge 0} }} then the corresponding probability is: | Given a k'-value, {{M|k'\in\mathbb{N}_{\ge 0} }} then the corresponding probability is: | ||
* {{MM|p:\eq 1-10^{-k} }} | * {{MM|p:\eq 1-10^{-k} }} | ||
− | === | + | ===Selected examples=== |
{| class="wikitable" border="1" | {| class="wikitable" border="1" | ||
|- | |- | ||
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| 0.9999 | | 0.9999 | ||
| ''9,999 in 10,000'' | | ''9,999 in 10,000'' | ||
+ | |- | ||
+ | ! {{M|\vdots}} | ||
+ | | colspan=4 | <center>{{M|\vdots}}</center> | ||
+ | |- | ||
+ | ! {{M|\infty}} | ||
+ | | colspan=2 | 0 (impossibility) | ||
+ | | colspan=2 | 1 (certainty) | ||
|} | |} | ||
==Purpose== | ==Purpose== |
Latest revision as of 16:09, 8 February 2018
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Contents
Definition
Given a probability, [ilmath]p\in[0,1]\subseteq\mathbb{R} [/ilmath] the corresponding values are:
- [math]k:\eq\frac{-\ln(p) }{\ln(10) } [/math], higher values indicate the event we have the probability for is rarer, eg [ilmath]k\eq 6[/ilmath] is 1 in 1,000,000 (1 million), or [ilmath]p\eq 0.000001[/ilmath]
- [math]k':\eq\frac{-\ln(1-p)}{\ln(10)} [/math], higher values indicate the event we have the probability for is more common, eg [ilmath]k'\eq 6[/ilmath] is 999,999 in 1,000,000, or [ilmath]p\eq 0.999999[/ilmath]
Given a k-value, [ilmath]k\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:
- [math]p:\eq 10^{-k} [/math]
Given a k'-value, [ilmath]k'\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:
- [math]p:\eq 1-10^{-k} [/math]
Selected examples
value, [ilmath]v[/ilmath] | [ilmath]v\ \mathbf{k} [/ilmath] (rarity) | [ilmath]v\ \mathbf{k}' [/ilmath] (commonality) | ||
---|---|---|---|---|
(As probability) | ||||
0 | 1 (certainty) | 0 (impossibility) | ||
1 | 0.1 | 1 in 10 | 0.9 | 9 in 10 |
2 | 0.01 | 1 in 100 | 0.99 | 99 in 100 |
3 | 0.001 | 1 in 1,000 | 0.999 | 999 in 1,000 |
4 | 0.0001 | 1 in 10,000 | 0.9999 | 9,999 in 10,000 |
[ilmath]\vdots[/ilmath] | | |||
[ilmath]\infty[/ilmath] | 0 (impossibility) | 1 (certainty) |