Two-Way Tables & Conditional Probability Cheat Sheet

Key Facts

• A two-way table shows counts or relative frequencies for two categorical variables, with row totals, column totals, and a grand total.
• A joint frequency is a count inside the table that belongs to both categories, such as $A$ and $B$ happening together.
• A marginal frequency is a row total or column total, and it represents the total number in one category.
• A joint probability is found with $P(A \cap B)=\frac{\text{count in both }A\text{ and }B}{\text{total count}}$.
• A marginal probability is found with $P(A)=\frac{\text{total count in }A}{\text{total count}}$.
• A conditional probability is found with $P(A\mid B)=\frac{P(A \cap B)}{P(B)}=\frac{\text{count in both }A\text{ and }B}{\text{total count in }B}$.
• Events $A$ and $B$ are independent if $P(A\mid B)=P(A)$, meaning event $B$ does not change the probability of event $A$.
• For events with nonzero probabilities, independence can also be checked using $P(A \cap B)=P(A)P(B)$.

Vocabulary

Two-way table

A table that displays data for two categorical variables by organizing counts into rows and columns.

Joint frequency

The count in one interior cell of a two-way table that belongs to both a row category and a column category.

Marginal frequency

A row total or column total in a two-way table.

Conditional probability

The probability that one event occurs given that another event has already occurred, written as $P(A\mid B)$.

Relative frequency

A proportion or percentage found by dividing a count by a relevant total.

Independent events

Events where knowing that one event occurred does not change the probability of the other event.