Difference between revisions of "K and k' values"
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m (Adding infinity case for 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
[hide]Definition
Given a probability, p∈[0,1]⊆R the corresponding values are:
- k:=−ln(p)ln(10), higher values indicate the event we have the probability for is rarer, eg k=6 is 1 in 1,000,000 (1 million), or p=0.000001
- k′:=−ln(1−p)ln(10), higher values indicate the event we have the probability for is more common, eg k′=6 is 999,999 in 1,000,000, or p=0.999999
Given a k-value, k∈N≥0 then the corresponding probability is:
- p:=10−k
Given a k'-value, k′∈N≥0 then the corresponding probability is:
- p:=1−10−k
Selected examples
| value, v | v k (rarity) | v k′ (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 |
| ⋮ | | |||
| ∞ | 0 (impossibility) | 1 (certainty) | ||
