# Lecture Slides April 21

Here’s the solution to the Tree Diagram problem we ended with:

Correction: solution is 3/6 + (3/6)*(3/5)*(2/4)+ (3/6)*(3/5)*(2/4)*(2/3)*(1/2)+(3/6)*(2/5)*(3/4)*(2/3)*(1/2)

## Final Exam Study Guide

### Featured

Here’s an assortment of problems from the sections that will be covered on the final exam.

You can use these problems to make a practice test. Make sure you also review test problems from the previous exams for material not included in the book chapters (like the Simplex method and Pascal’s triangle).

Chapter 1

• Section 1.2: 15, 17, 19, 39, 41, 43
• Section 1.3: 1,3,5, 9, 11

Chapter 2

• Section 2.1: 39, 41, 43, 49, 51
• Section 2.2: 17, 19, 21, 25, 27, 29, 37, 39
• Section 2.3: 33-49 (odds)
• Section 2.4: 1, 19, 21, 25
• Section 2.5: 1-9 (odds)

Chapter 3

• Section 3.1: 7, 10, 11, 13
• Section 3.2: 25-31 (odds), 33-41 (odds)
• Section 3.3: 22 (solution: operate refinery I for 4 days and refinery II for 3 days), 23 (see example 1 for a similar problem), 24, 25, 26 (solution: ship 4 cars from Baltimore to Philadelphia, 1 car from Baltimore to Trenton, and 6 cars from NY to Trenton), 31
• Make sure to review the Simplex method as it was presented in class
• Make sure to review finding vertices of higher dimensional feasible sets

Chapter 5

• Section 5.1: 1-13 odds only, 21-26, and 41-47 (do both even and odds for the last ten problems)
• Section 5.2: 15-38 odds only (here are examples where you are shading in a region on a Venn Diagram)
• Section 5.3: 11-19 (odds only), 26-30, 61-68 (these last four questions are similar to the flag example we did in class)
• Solutions for Section 5.3:
• solution to problem 26: 102,
• solution to problem 28: 52
• solution to problem 30: 68
• solution to problem 62: 36
• solution to problem 64: 56
• solution to problem 68: 40
• Section 5.4: 1-21 odds only, 37, 38 (The solution for number 38 is 2^5), 49
• Section 5.5: 21-29 odds, 29, 31, 34 (solution: 35*34*33*32*31),35, 37, 39, 49, 51, 61, 63
• Section 5.6: 1,3, 7, 9, 11, 13, 21
• Be sure to review Pascal’s Identity and Pascal’s Triangle!

Chapter 6

• Section 6.1: 1, 3, 11, 13, 15, 17, 19, 23
• Section 6.2: 11, 13, 19, 23, 25, 29, 31, 33, 35
• Section 6.3: 7, 9,11, 17 (Outcomes are recorded as sequence (a,b,c), in which a, b, and c are days of the week), 21, 25, 27, 29, 33
• Section 6.4: 1, 3, 5, 7, 9, 11, 13, 25, 33, 35, 37, 39, 43, 45, Challenge: 63
• Section 6.5: 1, 3, 5, 7, 9, 11, 13, 17, 25

Chapter 8

• Section 8.1: 7-17 (odds only), 19, 21, 23, 25
• Section 8.2: 7-15 odds only

# Extra Solutions

Here you’ll find an alternative solution to the card problem from our Tuesday review session. I’ve also included a solution to number 9 from Section 6.4.

# Study Guide Test 4

Here is a study check list for test 4:

• Definition of Experiment, Sample Space, Event, and Outcome
• Definitions of the intersection, union and complement of events
• Given an events $latex E$ and $latex F$, you should be able to explain in words what the event $latex E\cup F$, $latex E\cap F$ and $latex E’$ (See Section 6.1 homework)
• Know when two events are mutually exclusive.
• Know the definition of a probability distribution. (See Section 6.2 for lots of examples.)
• Know how to compute probability of an event, given that all outcomes are equally likely (See section 6.3)
• Know the inclusion-exclusion rule for probability: $latex Pr(E\cup F) = Pr(E) + Pr(F) – Pr( E\cap F)$ (See Example 11 from Section 6.2.)
• Use inclusion-exclusion to fill in a Venn Diagram (For some good problems see number 33 and 35 from Section 6.2 and numbers 1-8 from Section 6.4.)
• Know the complement rule: $latex Pr(E) = 1-Pr(E’)$
• Use the complement rule to compute probability
• Good clue to look for: `at least 1’…. See for example, the birthday example (example 6 in section 6.3)
• Know how to compute conditional probability (See Section 6.4)
• Know the definition of independence: Two events are independent if $latex Pr(E\cap F) = Pr(E)\cdot Pr(F)$ (See Section 6.4, problems 33-45)

# Test 3 Extra Credit

As promised, here is the extra credit I promised in class. Problems are based on some of the commonly missed problems from the test. The points will go toward your overall test grade.

The extra credit is due on March 31 at 10:15 AM. Late submissions will not be accepted.