---
title: 'Ch 2.1 Practice: Probability Basics'
author: "YOUR NAME HERE"
output:
  pdf_document: default
  html_document:
    df_print: paged
---

# 1. One hundred voters were asked their opinions of two candidates, $A$ and $B$, running for mayor. Their responses to three questions are: 65 said they like candidate $A$, 55 said they like $B$, and 25 said that they like both. 

## a. Draw a Venn diagram that depicts the above situation.



## b. What is the probability that someone likes neither?



## c. What is the probability that someone likes exactly one?


## d. What is the probability that someone likes at least one?


## e. What is the probability that someone likes at most one?



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# 2. Consider two events, $A$ and $B$, with $P(A)=0.4$ and $P(B)=0.7$. Determine the maximum and minimum values for $P(A\cap B)$ and the conditions under which of these values is attained.



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# 3. Let $A$ and $B$ be any two events defines on $S$. Suppose that $P(A)=0.4$, $P(B)=0.5$, and $P(A\cap B)=0.1$. What is the probability that $A$ or $B$ but not both occur?


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# 4. Let $A$ and $B$ be two events defined on $S$. If the probabity that at least one of them occurs is 0.3 and the probability that $A$ occurs but $B$ does not occur is 0.1, what is $P(B)$?






