4 min read•april 29, 2021

Josh Argo

Have you ever wondered how meteorologists determine the 🌧️ or ❄️ forecasts? What about the likelihood of a sports team winning a game? Analysts like meteorologists or sports analysts use probability models based on similar conditions in the past to *predict* the likelihood of these things happening in the present! In this unit, you will learn some basics of probability and get a taste of what these statisticians use everyday to keep us safe and 🤗.

Categorical Variables

The most common type of probability you will encounter in this unit will deal with **categorical variables**. Recall from __Unit 1__ and __Unit 2__, that categorical variables are often represented with *frequency tables* or *two-way tables (example pictured below)*. There are some important rules for determining probabilities from these types of displays that are essential to know in order to be successful on the AP exam.

Quantitative Variables

The other type of variable that you will encounter is **quantitative variables**. Quantitative variables will generally be dealt with using *density curves (example pictured below)***,** most notably the normal distribution. The normal distribution is the most useful tool in statistics and hinges on a good understanding of probability.

There are many important rules and conditions that come into play when determining the probability of certain events happening. In order to be successful on the AP Exam, it is important to familiarize yourself with these rules and conditions.

Independence

The most important probability condition that you need to be aware of is the concept of **independence**. This will also be essential as we progress to inferential statistics in Units 6-9.

For example, if I flip two coins, the likelihood of one landing on heads *is not affected *by the other coin. Therefore, we would say that these two events are independent. On the flip side, let’s consider temperature and snow likelihood. If the temperature is extremely low, the probability of it snowing will increase. Therefore, these two events are **not independent**, or **dependent**, since the temperature does affect the likelihood of snow.

Mutually Exclusive

Another key concept in probability is when two events are **mutually exclusive. **When two events are mutually exclusive, it means that it is impossible for them to occur at the same time.

To stay with our weather examples, the likelihood of having a hot day and snowing is impossible. Therefore, those two events are mutually exclusive.

There are three types of probability distributions we will mainly focus on in this unit: **normal distributions, binomial distributions and geometric distributions.** All of these have handy calculator functions that will make our work SO much easier! 😊

Normal Distribution

The most popular type of distribution in all data situations is the normal distribution. Whether it be ACT scores, heights of people or blood pressure levels, these all follow normal distributions and make it much easier to calculate where one data point compares to the rest of our data.

Binomial Distribution

Binomial distributions are events that involve four conditions:

- Two possible outcomes (binary)
- Independent trials
- Fixed number of trials
- All trials are equally likely of occurring

Binomial distributions come in handy when you want to determine the likelihood of a certain number of successes within our fixed number of trials.

For instance, if you wanted to determine the likelihood of flipping a coin 12 times and receiving 10 heads, a binomial distribution would be appropriate.

Geometric Distribution

A **geometric distribution** is very similar to a binomial distribution, with the only difference being that *we do not have a fixed number of trials.* A geometric distribution typically involves repeating an action until you get a success.

For example, if we flip a coin *until we get a heads* this would represent a geometric distribution.

🎥 **Watch: AP Stats**** Unit 4**

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Unit 1: Exploring One-Variable Data

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Unit 2: Exploring Two-Variable Data

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Unit 3: Collecting Data

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Unit 4: Probability, Random Variables, and Probability Distributions

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Unit 5: Sampling Distributions

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Unit 6: Inference for Categorical Data: Proportions

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Unit 7: Inference for Qualitative Data: Means

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Unit 8: Inference for Categorical Data: Chi-Square

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Unit 9: Inference for Quantitative Data: Slopes

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