# Finite Math—Semester B

Normal is overrated, but normal distributions aren't.

*Shmoop's Finite Math course has been granted a-g certification, which means it has met the rigorous iNACOL Standards for Quality Online Courses and will now be honored as part of the requirements for admission into the University of California system.*

When it comes down to it, life is all about luck. Whether you find twenty bucks sitting on the sidewalk or get struck by lighting, chance plays a bigger role in life than people admit. Even the very best Dungeon Masters and Texas Hold 'Em champions can't escape probability at work. Unless they're cheating.

In this Common Core-aligned course, we'll delve deep into the mysteries of counting theory, normal distributions, why so many people you know share the same birthday, and more. We'd tell you what else we'll cover, but we don't want to ruin the mystery.

On second thought, let's ruin the mystery. With loads of drills, examples, and projects, we'll cover

- counting theory, Venn diagrams, and other ways to deal with large sets of numbers.
- probability, experiments, and the famous Birthday Problem.
- conditional probability, events, and using trees to represent them.
- statistics, histograms, odds, and binomial events.
- normal distributions, z-scores, and game theory.

What are the odds you'll finish this course knowing all there is to know about statistics and probability? We're betting pretty good.

P.S. Finite Math is a two-semester course. You're looking at Semester B, but you can check out Semester A here.

### Technology Requirements

Technology-wise, all you'll need to complete this course is a computer with internet access (a tablet is ok, too), your internet browser of choice, and your calculator of choice (Google works in a pinch). Experience with all these tools will come in handy, too, but if you don't have any, you'll pick it up soon, we promise.

## Course Breakdown

### Unit 8. Counting Theory

You learned how to count back in preschool, so it's high-time you stepped up your counting game. We'll start out with sets, unions, and intersections, and even draw a few Venn diagrams. Then, we'll get factorials involved and talk about combinations and permutations and their many applications. By the time we're through, you'll be able to give the Count a run for his money.

### Unit 9. Probability

If probabilistic thinking is already intuitive to you, then great. You're ahead of the game. But for the rest of us, this unit is all about making probability as intuitive as how to eat the last Oreo. (Twist-and-lick, obviously.) From setting up experiments to probability properties and formulas, this unit contains more coin tosses and die rolls than you thought were possible.

### Unit 10. Conditional Probability

In this unit, we're going to learn how to tell if that third flip being heads depends on the first two being heads (spoiler alert: no). With the help of the Product Rule, trees, and Bayes' Theorem, we'll learn about a new kind of probability: one where the likelihood of an outcome can change in an instant—or at least in the blink of another event happening first.

### Unit 11. Statistics

We'll kick off the unit by discussing how to turn any kind of data into a table or graph that you trust. (Those histograms always looked a little shady to us.) After talking about probability and odds, we'll boil down our data into bite-sized summaries, like expected value, variance, and standard deviation. They're not as tasty as those mini-quiches and shrimp cocktails, but we promise they'll be more useful when it comes to data analysis.

### Unit 12. Normal Distributions and Game Theory

We won't lie to you: this unit's a biggie. Often, normal distributions can seem more abnormal than you'd think. Don't worry. We'll help you tackle with z-scores, bell curves, and binomial probabilities like a boss. After that, we'll take on game theory, talk about its different strategies, and learn how to kick your opponent's butt at *Monopoly*. Family game night will never be the same again.

## Sample Lesson - Introduction

#### Lesson 5: Probability Applied

Besides potentially encouraging gambling addictions in classrooms across the nation through the copious use of dice examples, probability can be applied to actual, real-life scenarios as well. Namely, to help us make good choices in life. Such as deciding to skip the craps table after losing five nights in a row. Or helping us to interpret the results of studies published in the news. Or deciding whether or not our secret admirers actually admire us.

Wait, you didn't put that note in our locker?

By combining what we know about biased versus unbiased experimental designs and experimental versus non-experimental probabilities, we are now the new kids on the block. By which we mean: no one's going to put anything by us.

- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 10, 11, 12
- Course Type: Basic
- Category:
- Math
- High School

- Prerequisites:

Algebra II—Semester A (2014-2015)

Algebra II—Semester B (2014-2015)

Finite Math—Semester A

Algebra I—Semester A

Algebra I—Semester B

Just what the heck is a Shmoop Online Course?

Courses Tutorial

### Common Core Standards

The following Common Core Standards are covered in this course:

CCSS.Math.Content.1.MD.A.1CCSS.Math.Content.2.MD.B.5

CCSS.Math.Content.HSA-APR.C.5

CCSS.Math.Content.HSS-CP.A.1

CCSS.Math.Content.HSS-CP.A.2

CCSS.Math.Content.HSS-CP.A.3

CCSS.Math.Content.HSS-CP.A.4

CCSS.Math.Content.HSS-CP.A.5

CCSS.Math.Content.HSS-CP.B.6

CCSS.Math.Content.HSS-CP.B.7

CCSS.Math.Content.HSS-CP.B.8

CCSS.Math.Content.HSS-CP.B.9

CCSS.Math.Content.HSS-IC.A.1

CCSS.Math.Content.HSS-IC.A.2

CCSS.Math.Content.HSS-IC.B.3

CCSS.Math.Content.HSS-IC.B.4

CCSS.Math.Content.HSS-IC.B.5

CCSS.Math.Content.HSS-IC.B.6

CCSS.Math.Content.HSS-ID.A.1

CCSS.Math.Content.HSS-ID.A.2

CCSS.Math.Content.HSS-ID.A.4

CCSS.Math.Content.HSS-ID.B.5

CCSS.Math.Content.HSS-ID.C.7

CCSS.Math.Content.HSS-MD.A.1

CCSS.Math.Content.HSS-MD.A.2

CCSS.Math.Content.HSS-MD.A.4

CCSS.Math.Content.HSS-MD.B.5

CCSS.Math.Content.HSS-MD.B.6

CCSS.Math.Content.HSS-MD.B.7