Homework_3_fires_AH_EP.Rmd

---
title: "Homework 3"
author: "Andrea Hemmelmann - Eric Parra"
date: "23 november 2018"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Bayes' rule exercise

## Problem formulation

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?

## Solution

p= Probability

Bayes' rule = p(H|D) = (p(D|H)) p(H)) / p(D)

Where p(D)= (p(D|H)) p(H)) + (p(D|H_f)) p(H_o))

Posterior = (Likelihood * Prior) / Evidence

Where H= Wildfire caused by a lightning. D= Witness said the wildfire was caused by a lightning

## Creating variables

```{r}

p_h <- 0.001 # Probability that the wildfire was caused by lightning
p_h_o <- 0.999 #Probability that the wildifre was not caused by a lightning
p_d_h <- 0.8 # Probability that the witness is correct
p_d_h_f <- 0.2 # Probability that the witness is wrong

```

## Bayes' rule calculation

Now we calculate the probability that the witness claim is correct by assign the variables values to the Bayes' Rule equation

```{r}

p_l_w = (p_d_h * p_h) / ((p_d_h * p_h) + (p_d_h_f * p_h_o))
p_l_w_p = p_l_w * 100
p_l_w_p

```
Therefore the probability that the witness claim is correct is 0.4%