Statistics and probability

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.
Intro to probability
We give you an introduction to probability through the example of flipping a quarter and rolling a die.
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.
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.
Simple probability
Practice finding probabilities of events, such as rolling dice, drawing marbles out of a bag, and spinning spinners.
Experimental probability
Based on past experience, we can make reasonable estimates of the likelihood of future events.
Experimental probability
Practice making reasonable estimates of the likelihood of future events based on past experience.
Intuitive sense of probabilities
Think about what probabilities really mean. What does a probability of 0 mean? How about 1?
Comparing probabilities
Practice expressing probabilities in different forms (fractions, decimals, and percents).

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.
Reasonable samples
To make a valid conclusion, you'll need a representaive, not skewed, sample.
Valid claims
Practice figuring out whether we took a random sample and whether we're able to draw valid conclusions from our data.
Making inferences from random samples
Given a random sample, practice figuring out what can we reasonably infer about the entire population?
Comparing distributions with dot plots (example problem)
Sal examines two distributions in dot plots to draw conclusions about the times of Olympic swimmers.
Comparing distributions
Practice comparing distributions that are presented in dot plots, histograms, and box plots.