Two-Way Table Probability

1) Read the table carefully

A two-way table organizes data by two categories at the same time. One direction usually shows one category, and the other direction shows the second category. Probabilities come from the counts in the table.

2) Find the right total

To answer a probability question, first identify:

• the event asked for, and
• the total number of outcomes in the whole table or in the stated group.

Use:

• single event probability = favorable count ÷ total count
• conditional probability = favorable count within the given group ÷ total count of that group

3) Simplify the answer

Write the probability as a fraction first, then simplify fully. If a decimal or percent is not requested, keep the exact fraction.

4) Watch for “given that”

Phrases like “given,” “among,” “of those,” or “if” usually mean you should use only part of the table, not the grand total.

5) Check your work

Make sure your numerator is a count that matches the question, and your denominator is the correct total. The probability should always be between 0 and 1.

Quick strategy

1. Locate the relevant row, column, or full table.
2. Count the favorable outcomes.
3. Count the correct total.
4. Form and simplify the fraction.