P(A) = P(A and B) + P(A and Bc) @jbstatistics

Uploaded March 2019 | Updated September 2026, 1 hour ago

A quick video to illustrate that P(A) = P(A and B) + P(A and Bc), and work through a simple conditional probability example that makes use of this identity.

I know from experience that some of my students have trouble seeing this (especially when it comes up in a formulaic approach to a problem), and I wanted to have a video that I could point them to.

My Law of Total Probability video is here: youtu.be/7t9jyikrG7w

Introduction to the Central Limit Theorem

Hypothesis Tests for One Population Variance

Pooled-Variance t Tests and Confidence Intervals: An Example

Deriving the Mean and Variance of a Continuous Probability Distribution

Using R to Find Chi-square Areas and Percentiles

An Introduction to the t Distribution (Includes some mathematical details)

Simple Linear Regression: Inference on the Slope (An Example) (Old, fast version)