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Contingency Table Visualization

2×2 contingency table showing joint, marginal, and conditional probabilities. Click any cell to highlight it.

Joint Probability Table

BBcTotal
A
0.4200
P(A ∩ B)
0.1800
P(A ∩ Bc)
0.6000
Ac
0.1200
P(Ac ∩ B)
0.2800
P(Ac ∩ Bc)
0.4000
Total0.54000.46001.0000

Conditional on A

Click rows to highlight paths
P(B|A) = P(A∩B) / P(A) = 0.42 / 0.600.7000
P(Bc|A) = P(A∩Bc) / P(A) = 0.18 / 0.600.3000
Total1.0000

Conditional on Ac

Click rows to highlight paths
P(B|Ac) = P(Ac∩B) / P(Ac) = 0.12 / 0.400.3000
P(Bc|Ac) = P(Ac∩Bc) / P(Ac) = 0.28 / 0.400.7000
Total1.0000

Conditional on B

Click rows to highlight paths
P(A|B) = P(A∩B) / P(B) = 0.42 / 0.540.7778
P(Ac|B) = P(Ac∩B) / P(B) = 0.12 / 0.540.2222
Total1.0000

Conditional on Bc

Click rows to highlight paths
P(A|Bc) = P(A∩Bc) / P(Bc) = 0.18 / 0.460.3913
P(Ac|Bc) = P(Ac∩Bc) / P(Bc) = 0.28 / 0.460.6087
Total1.0000
How to read: The main table shows joint probabilities P(A∩B) in each cell. Row and column totals show marginal probabilities. The four tables on the right show all conditional probability distributions with their calculations. Click any conditional probability to highlight the corresponding cells in the main table.

Reading Contingency Tables
Conditional Probability Formula
Applications in Statistics



Understanding Conditional Probability with Contingency Tables

Contingency tables organize probabilities in a 2×2 grid showing how two events relate. Joint probabilities appear in cells, marginal probabilities in row and column totals. Click any conditional probability to see how it's calculated as a ratio of the intersection to the conditioning event.



Reading Contingency Tables

A 2×2 contingency table displays all probability relationships in one view. The four inner cells show joint probabilities P(A∩B), while row and column totals show marginal probabilities P(A) and P(B).
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Conditional Probability Formula

The table makes P(A|B) = P(A∩B) / P(B) visual and concrete. Click any conditional probability to see both the numerator (intersection) and denominator (marginal total) highlighted in the main table.
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Applications in Statistics

Contingency tables are fundamental in statistics for analyzing categorical data, testing independence, and understanding relationships between variables in surveys, medical studies, and experimental research.
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