# Statistics and probability

Contents

This introduction to probability and statistics explores probability models, sample spaces, compound events, random samples, and a whole lot more.

## Basic probability

Flip a quarter a hundred times. What's the probability that it will turn up heads? Tails? Even if we are unsure about whether something will happen, can we start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others) occurring. This tutorial will introduce us to the tools that allow us to think about random events and the logic behind comparing, judging, and finding the probabilities of those events.

8:18

Intro to probability

We give you an introduction to probability through the example of flipping a quarter and rolling a die.

2:56

Simple probability: yellow marble

In order to find the probability of picking a yellow marble from a bag, we have to first determine the number of possible outcomes and how then many of them meet our constraints.

9:56

Simple probability: non-blue marble

In this example we are figuring out the probability of randomly picking a non-blue marble from a bag. Again, we'll have to think about the possible outcomes first.

Exercise

Simple probability

Practice finding probabilities of events, such as rolling dice, drawing marbles out of a bag, and spinning spinners.

6:55

Experimental probability

Based on past experience, we can make reasonable estimates of the likelihood of future events.

Exercise

Experimental probability

Practice making reasonable estimates of the likelihood of future events based on past experience.

8:51

Intuitive sense of probabilities

Think about what probabilities really mean. What does a probability of 0 mean? How about 1?

Exercise

Comparing probabilities

Practice expressing probabilities in different forms (fractions, decimals, and percents).

## Probability models

In many situations, we don't know exact probabilities, so we estimate probability based on history of events.

7:02

Theoretical and experimental probabilites

Compare expected probabilities to what really happens when we run experiments.

5:05

Making predictions with probability

Predict the number of times a spinner will land on an elephant.

Exercise

Making predictions with probability

Practice predicting the number of times a certain event will happen.

7:25

Probability models example: frozen yogurt

Model the probability of a frozen yogurt line having 0, 1, or 2 people in it.

Exercise

Probability models

Practice creating probability models and understand what makes a valid probability model.

## Compound events and sample spaces

9:10

Sample spaces for compound events

Explore the notion of a "sample space". See a sample space represented as a tree diagram, table, and list.

Exercise

Sample spaces for compound events

Practice checking if sample space diagrams match a compound event.

5:15

Die rolling probability

We're thinking about the probability of rolling doubles on a pair of dice. Let's create a grid of all possible outcomes.

5:03

Probability of a compound event

Learn how to use sample space diagrams to find probabilities.

Exercise

Probabilities of compound events

Practice using sample space diagrams to find probabilities.

2:35

Counting outcomes: flower pots

Find the number of ways you can put four types of flowers into three types of pots.

4:31

Count outcomes using tree diagram

We'll use a tree diagram to visualize and count all the possible outcomes. This helps us to determine the probability.

Exercise

The counting principle

Practice counting possible outcomes in a variety of situations. These problems cover everything from counting the number of ways to get dressed in the morning to counting the number of ways to build a custom pizza.

## Comparing and sampling populations

When we are trying to make a judgement about a population, it is often impractical (or impossible) to observe every member of the population. Imagine trying to survey all 300+ million Americans to understand the likely outcome of the next presidential election! Because of this, much of statistics is collecting data from a representative and random sample. From the data collected from this random sample we can infer things about the greater population.

4:17

Reasonable samples

To make a valid conclusion, you'll need a representaive, not skewed, sample.

Exercise

Valid claims

Practice figuring out whether we took a random sample and whether we're able to draw valid conclusions from our data.

Exercise

Making inferences from random samples

Given a random sample, practice figuring out what can we reasonably infer about the entire population?

4:00

Comparing distributions with dot plots (example problem)

Sal examines two distributions in dot plots to draw conclusions about the times of Olympic swimmers.

Exercise

Comparing distributions

Practice comparing distributions that are presented in dot plots, histograms, and box plots.