Conditional Probability Calculator

Condition Name:

Outcome Name:

Frequency Table (Counts)

	Test+	No Test+	Total
Disease	0.0095	0.0005	100
No Disease	0.0495	0.9405	9900
Total	590	9410	10000

Conditional Probabilities Given Disease

Given Condition	Test+	No Test+	Total
Disease	95.0% P(Test+\|Disease)	5.0% P(No Test+\|Disease)	100%
No Disease	5.0% P(Test+\|No Disease)	95.0% P(No Test+\|No Disease)	100%

Conditional Probability Calculations

P(Test+ | Disease)

= 95 / 100

95.0%

P(Test+ | No Disease)

= 495 / 9900

5.0%

P(Disease | Test+)

= 95 / 590

16.1%

P(No Disease | Test+)

= 495 / 590

83.9%

Understanding the Results

Key Insight: Conditional probability focuses on a subset of the data. When we calculate P(B|A), we only look at the rows/columns where A occurred.

How to read contingency tables for conditional probability:

P(Outcome | Condition): Look at the condition row, divide the intersection by the row total
P(Condition | Outcome): Look at the outcome column, divide the intersection by the column total
The intersection cell represents both events happening together
Marginal totals show the unconditional probabilities

Medical Test Interpretation: Even with a 95% accurate test, a positive result only gives 16.1% chance of actually having the disease. This is because the disease is rare (1% prevalence), so most positive tests are false positives.