Exercie_3.Rmd

---
title: "Homework - Bayer´s Rule"
author: "René Neuling - Jakob Feyrer"
date: "25 November 2018"
output: html_document
---


# Exercise Bayer´s Rule
## Task

Assume that lightning strike causes wildfires with a probability of 1/1000. You observe a wildfire and an eyewitness claims that it was lit by lightning. What is the probability that this is correct, knowing that eyewitness reports are reliable 80% of the time?




## Define all Parameters and describe Bayer´s law

we have a wildfire because of a lithning
lithning was the trigger and was seen with conditional probability of Bayer´s rule

If we write Bayer´s rule in words:

Posterior = Likelihood × Prior / Evidence # to see in lecture 4 

Bayer´s rule = P(L|W) = L(W|L) * P(L) / P(W)

P(W) = PW(W|L) * P(L) + P(L|W_c) * P(W_c)

P_L = 0.001 # probability, that the wildfire was caused be lithning  
P_W_c = 1 - P_L = 0.999 # probability of wildfire caused be another faktor  
P_L_W = 0.8  # withness of a report, that the wildfire was caused be lithning  
P_L_K_c = 0.2 # # probability that the eyewithness is wrong  

# now we have defined all parameters and can calcute
## Because we have a probability, we have to multiply the result with 100

P(L|W) = (P_W_L * P_L) / (P_W_L * P_L) + (P_L_c * P_W_c) * 100 


The probability, that the wildfire was caused be lithning with knowing, that was seen is 0.4%