---
title: "Homework assignment #2"
author: "Milica Cudina"
date: "`r Sys.Date()`"
output: pdf_document
---
<!-- The author of this template is Dr. Gordan Zitkovic.-->
<!-- The code chunk below contains some settings that will  -->
<!-- make your R code look better in the output pdf file.  -->
<!-- If you are curious about what each option below does, -->
<!-- go to https://yihui.org/knitr/options/ -->
<!-- If not, feel free to disregard everything ...  -->
```{r echo=FALSE, warning=FALSE, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.align="center",
  fig.pos="t",
  strip.white = TRUE
)
```
<!-- ... down to here. -->

# More probability review
## Problem #1. **(5 points)**
Let $E$ and $F$ be any two events. If
\begin{equation}%\label{}
    \nonumber
    \begin{split}
      \mathbb{P}[E] = \mathbb{P}[F] = \frac{2}{3}\,,
    \end{split}
\end{equation}
then $E$ and $F$ cannot be mutually exclusive. *True or false? Why?*

## Problem #2. **(5 points)**
If events $A$ and $B$ are mutually exclusive, they are necessarily independent. *True or false? Why?*

## Problem 3. **(5 points)**
A test is used to determine whether people exhibiting green spots have the *duckpox* or not. It is believed that at any given time 4% of people exhibiting green spots actually have the *duckpox*. 
The test is 99% accurate if a person actually has the *duckpox*. The test is 96% accurate if a person does **not** have the *duckpox*. What is the probability that a randomly selected person who tests positive for the *duckpox* actually has the *duckpox*?

---


# Textbook problems on the binomial
## Problem 1. **(a is 4 points; b is 2 points; c is 2 points; d is 3 points; e is 4 points=15 points total)**<br>
Solve **Problem 4.18** from the textbook.

## Problem 2. **(a is 3 points; b is 2 points; c is 3 points = 8 points total)** 
Solve **Problem 4.22 (a, b, c) ** from the textbook.

## Problem 3. **(2 points each)** 
Solve **Problem 4.24 (a, b, c)** from the textbook.

## Problem 4. **(2 points each)** 
Solve **Problem 4.26** from the textbook.