Practice Two-Way Tables in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A table that displays frequencies for two categorical variables simultaneously, organized with one variable in rows and the other in columns. It shows joint frequencies (individual cells), marginal frequencies (row/column totals), and enables calculation of conditional frequencies.

Imagine surveying students about their favorite sport AND their grade level. A two-way table is like a grid: grades go down the side, sports go across the top, and each cell tells you how many students are in that specific combination. The totals on the edges (margins) tell you the overall counts for each category.

Example 1

medium
A two-way table shows: Smoker/Cancer=30, Smoker/No-Cancer=70, Non-smoker/Cancer=20, Non-smoker/No-Cancer=180. Calculate marginal and joint proportions, and find P(Cancer|Smoker) vs P(Cancer|Non-smoker).

Example 2

hard
From a 2×2 table: Group/Outcome frequencies: A-Success=40, A-Fail=10, B-Success=25, B-Fail=25. Test independence using the chi-square approach and calculate the relative risk.

Example 3

easy
A two-way table: Left-handed/Male=12, Left-handed/Female=8, Right-handed/Male=88, Right-handed/Female=92. Find the marginal proportion of left-handers and P(Left-handed|Male).

Example 4

hard
Construct a two-way table from this information: 200 students surveyed; 120 prefer online learning; 80 prefer in-person. Of online learners: 90 passed. Of in-person learners: 55 passed. Complete the table and find whether learning mode and passing are independent.
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