Basic Concepts of Probability: KEY TAKEAWAYS | Saylor Academy

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Read this section about basic concepts of probability, including spaces, and events. This section discusses set operations using Venn diagrams, including complements, intersections, and unions. Finally, it introduces conditional probability and talks about independent events.

A conditional probability is the probability that an event has occurred, taking into account additional information about the result of the experiment.
A conditional probability can always be computed using the formula in the definition. Sometimes it can be computed by discarding part of the sample space.
Two events $A$ and $B$ are independent if the probability $P(A \cap B)$ of their intersection $A \cap B$ is equal to the product $P(A) \cdot P(B)$ of their individual probabilities.

COURSE INTRODUCTION

Course Syllabus

Unit 1: Statistics and Data

1.1.1: What is Statistics?

What are Statistics?

1.1.2: Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

Basic Definitions and Concepts

1.1.3: Types of Data and Their Collection

Variables and Data Collection

Presenting Data

1.2.1: Graphical Methods for Describing Quantitative Data

Graphing

Three Popular Data Displays

1.2.2: Numerical Measures of Central Tendency and Variability

Numerical Measures of Central Tendency and Variability

Measures of Central Location

Mean, Median, Mode, and Variance

1.2.3: Methods for Describing Relative Standing

Percentiles

1.2.4: Methods for Describing Bivariate Relationships

Scatterplots and Bivariate Data

Pearson's r

Unit 1 Assessment

Unit 1 Assessment

Unit 2: Elements of Probability and Random Variables

2.1.1: Events, Sample Spaces, and Probability

Introduction to Probability

Basic Concepts of Probability

2.1.2: Counting Rules

Permutations and Combinations

The Addition Rule for Probability with a Venn Diagram Example

2.2.1: Common Discrete Random Variables

Random Variables and Probability Distributions

Binomial Distributions

Binomial, Poisson, and Multinomial Distributions

2.2.2: Normal Distribution

The Standard Normal Distribution

More on Normal Distributions

Introduction to the Normal Distribution

Unit 2 Assessment

Unit 2 Assessment

Unit 3: Sampling Distributions

3.1.1: Continuous Random Variables

Continuous Random Variables

3.1.2: Definition and Interpretation

Introduction to Sampling Distributions

3.1.3: Sampling Distributions Properties

Wolfram Demonstrations Project

3.2.1: The Sampling Distribution of Sample Mean

The Sampling Distribution of a Sample Mean

The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean

Sampling Distribution

3.2.2: The Sampling Distribution of Pearson's r

Sampling Distribution of r

3.2.3: The Sampling Distribution of the Sample Proportion

Sampling Distribution of p

Standard Deviation

Unit 3 Assessment

Unit 3 Assessment

Unit 4: Estimation with Confidence Intervals

4.1.1: Sample Statistics and Parameters

Basic Sample Statistics and Parameters

4.1.2: Bias and Sampling Variability

Characteristics of Estimators

4.2.1: Confidence Intervals for Mean

Confidence Intervals for the Mean

Demonstration: Confidence Intervals for a Mean

t Distribution Demonstration

Comparing Normal and Student's t-Distributions

4.2.2: Confidence Intervals for Correlation and Proportion

Confidence Intervals for Correlation and Proportion

Confidence Intervals

Unit 4 Assessment

Unit 4 Assessment

Unit 5: Hypothesis Test

5.1.1: Setting up Hypotheses

Setting Up Hypotheses

5.1.2: Interpreting Hypotheses Testing Results

The Observed Significance of a Test