https://github.com/arthurkushman/total_probability
Total probability + Thomas Bayes, Bernoulli distribution formulas
https://github.com/arthurkushman/total_probability
bayes bernulli formulas math mathematics php probability
Last synced: 8 months ago
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Total probability + Thomas Bayes, Bernoulli distribution formulas
- Host: GitHub
- URL: https://github.com/arthurkushman/total_probability
- Owner: arthurkushman
- License: mit
- Created: 2017-01-30T13:45:13.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2019-05-03T15:39:45.000Z (about 7 years ago)
- Last Synced: 2025-10-08T02:02:49.528Z (9 months ago)
- Topics: bayes, bernulli, formulas, math, mathematics, php, probability
- Language: PHP
- Homepage:
- Size: 1.12 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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## Total probability + Thomas Bayes, Bernoulli distribution formulas
This project was created for those folks who love Math + PHP and either want to have
a great library to work with Total probability and Bayes, Bernoulli formulas
to calculate any real-world tasks on demand.
* [Total probability](#user-content-total-probability)
* [Thomas Bayes](#user-content-thomas-bayes)
* [Bernoulli distribution](#user-content-bernoulli-distribution)
### Examples
#### Total probability
We have 3 baskets:
- 1-st basket contains 7 black and 4 white balls
- 2-nd basket contains only white balls
- 3-d basket contains only black balls
What's the probability of taking a black ball?
The basket choice is 1/3.
- In the 1st basket we've got 7/11(7+4) probability of taking black ball.
- In 2nd basket there are only white balls - probability is 0.
- In 3d basket there are only black balls - probability is 1.
So we execute ```totalProbability``` method from ```Formula``` class:
```php
$this->formula = new Formula();
$result = $this->formula->totalProbability(
[0.33, 0.33, 0.33],
[0, 1, 0.45],
]);
echo $result; // 6/11=0.(54)
```
#### Thomas Bayes
At the warehouse came 2 party products:
- 1st - 4000 items
- 2nd - 6000 items
The percent of a non-standard items in 1st party is 20%
The percent of a non-standard items in 1st party is 10%
Randomly taken item of two parties turned out to be standard - what's the probability
relation of this item to 1st and 2nd party.
Part 1:
Overall items at the warehouse: 4000 + 6000 = 10000 -> 4000/10000 = 0.4, 6000/10000 = 0.6
Check: 0.4+0.6=1
- 1st party has standard items -> 100% - 20% = 80% standard items -> 80/100 = 0.8
- 2nd party has standard items -> 100% - 10% = 90% standard items -> 90/100 = 0.9
Using total probability formula:
```php
$this->formula = new Formula();
$result = $this->formula->totalProbability([0.4, 0.8], [
0.8,
0.9
]);
echo $result; // 0.86
```
We've got the probability, that the any picked item will be standard.
Then using Bayes formula:
```php
$result = $this->formula->bayesProbability(0.4, 0.8, 0.86);
echo $result; // 0.37
```
We've got a probability, that the selected standard item will be related to 1st party.
```php
$result = $this->formula->bayesProbability(0.6, 0.9, 0.86);
echo $result; // 0.63
```
We've got a probability, that the selected standard item will be related to 2nd party.
Check: 0.37+0.63=1
#### Bernoulli distribution
Find the probability, that within 10 flips of a coin tails will result in 3 times.
Using combinatorial combinations function 10! / 7! * 3! = 120
and combining it with Bernoulli distribution formula ```Cmn * p^m * q^n-m``` - getting the result:
```php
$result = $this->formula->independentProbability(10, 3, 0.5);
echo $result; // 0.1171875
```
We've got a probability, that withing 10 flips of a coin tails will result in 3 times.
#### The probability of the relative frequency deviation of the probability