Key Probability Concepts and Rules

Add Law

To find the chance of A or B, add both, then subtract the overlap. P(A or B) = P(A) + P(B) − P(A and B)

Probability Rules

Probabilities must be between 0 and 1, and all possible outcomes must add up to exactly 1.

Bayes' Trick

A way to update the chance of something after learning new info. ("What's the chance now that I know this?")

Equal Odds Method

If every outcome is equally likely, split the probability evenly.

Combo Count

How many ways you can choose items when order doesn't matter.

Not A

Everything that's not in A. (If A is "rolled a 3," Not A is "rolled anything but 3.")

If-Given Chance

The chance of A given B already happened. P(A|B) = P(A and B) / P(B)

Event Set

A group of outcomes you're interested in. (e.g., "rolling an even number" is an event.)

No Link Events

A and B don't affect each other. P(A|B) = P(A) and vice versa.

A and B (Overlap)

Both A and B happen. This is their intersection. P(A ∩ B)

Both Happen (Joint)

The chance of A and B happening together.

Single Event Odds (Marginal)

Just A or just B, ignoring anything else. Usually found in the margins of a table.

Step-by-Step Test

An experiment with multiple steps. Total outcomes = multiply the number of outcomes at each step.

Multiply Rule

To find the probability of A and B happening, multiply P(A) by P(B|A) if they're dependent, or just P(A) × P(B) if they're independent.

No Overlap

A and B can't happen at the same time. P(A ∩ B) = 0

Order Matters (Permutation)

How many ways to pick and arrange items when order counts.

Updated Odds (Posterior)

New probabilities after getting more info (like after using Bayes' Rule).

Starting Odds (Prior)

Your best guess before learning anything new.

Chance Number (Probability)

A number from 0 to 1 that tells how likely something is.

Luck Test (Random Experiment)

A process where the outcome is unpredictable but well-defined.

Past Data Method (Relative Frequency)

Use data to estimate probability from how often something happened before.

Single Outcome (Sample Point)

One specific result, like "rolled a 5."

All Outcomes (Sample Space)

The complete list of all possible results.

Gut Method (Subjective)

Probabilities based on judgment or opinion, not data.

Branch Chart (Tree Diagram)

A visual of step-by-step choices to show all possible paths and their probabilities.

A or B (Union)

Anything in A, B, or both. P(A ∪ B)

Circle Map (Venn Diagram)

A picture with circles to show how events relate (overlap, separate, etc.).