Rows show the categories of one variable (e.g. Boy/Girl), columns show categories of a second variable (e.g. Walk/Bus). Each inside cell is a joint frequency (fits both categories); each row/column total is a marginal frequency; the bottom-right cell is the grand total.

If a row or column has only one unknown cell, subtract the known values from that row/column's total. Work outward until every cell is filled.

Example: If the Boys row totals $135$ and "Walk" is $72$, then Boys who take the Bus $=135-72=63$.

Example: $P(\text{Walk}) = \dfrac{174}{300}$. $P(\text{Boy and Bus}) = \dfrac{63}{300}$.

The condition restricts the sample space to just that row or column total — not the grand total.

Example: Find $P(\text{Walk} \mid \text{Boy})$.

1. Restrict to the "Boy" row: total $=135$.
2. Favourable outcome within that row: Boys who walk $=72$.
3. $P(\text{Walk}\mid\text{Boy}) = \frac{72}{135}$

As a fraction, decimal, or percentage — simplified where possible. Writing "72 out of 135" or a ratio like "72:135" is not accepted as a probability.

They display the exact same information in different layouts — every terminal node of a frequency tree corresponds to one joint-frequency cell in a two-way table. If a question's wording is easier to follow sequentially (first split by one category, then by the second), build a frequency tree first and transfer the results into the table afterwards; if the categories are better understood as a grid from the outset, go straight to the table.

$250$ students were asked if they play an instrument. $140$ are girls; $90$ students in total play an instrument; $55$ boys do not play an instrument. Find $P(\text{plays an instrument} \mid \text{boy})$.

1. Boys total: $250-140=110$.
2. Boys who play: $110-55=55$.
3. $P(\text{plays}\mid\text{boy}) = \frac{55}{110} = \frac12$