Conditional Probability Calculator

Calculator Inputs

Use counts from a table, or enter direct probabilities.

Input Mode

Event A Name

Event B Name

Total Observations

Event A Count

Event B Count

Both Events Count

Probability Scale

P(A)

P(B)

P(A and B)

Decimal Precision

Formula Used

The main formula is P(A | B) = P(A and B) / P(B). The denominator must be greater than zero.

The reverse condition is P(B | A) = P(A and B) / P(A). The union is P(A or B) = P(A) + P(B) - P(A and B).

For count data, the script first converts each count into a probability. For example, P(A) equals Event A count divided by total observations.

How to Use This Calculator

Select count mode when you have a data table.
Select probability mode when values are already known.
Enter names for Event A and Event B.
Fill the values required by your selected mode.
Choose decimal precision for displayed results.
Press Calculate to show results below the header.
Use CSV or PDF downloads for reports.

Example Data Table

Total	Purchased	Clicked Ad	Purchased and Clicked	P(Purchased \| Clicked)
200	90	120	75	75 / 120 = 0.6250
500	180	250	130	130 / 250 = 0.5200
1000	420	600	330	330 / 600 = 0.5500

Conditional probability helps explain how one event changes another event's chance. It is useful when events are linked. A card draw, medical test, survey result, or quality check can all need this idea. The calculator turns raw counts or probability values into clear results. It also shows related measures. These measures help you compare dependence, complements, and combined event behavior.

What Conditional Probability Means

Conditional probability measures the chance of event A after event B is already known. It does not ask for the general chance of A. It asks for a filtered chance inside the B group. This makes the method powerful for real data. You can study buyers who clicked an ad. You can review students who passed a prerequisite. You can also inspect machines that failed one test before another.

Why This Calculator Helps

Manual work can be simple at first. Yet errors appear when decimals, percentages, and counts mix together. This tool keeps the steps organized. Enter counts from a table, or enter direct probabilities. The script validates impossible values. It then returns P(A), P(B), P(A and B), P(A given B), and P(B given A). It also checks the difference between observed overlap and the independent overlap.

Using Results Wisely

A high conditional probability does not prove cause. It shows association under the selected condition. Always check the sample size and data source. Small samples can create unstable percentages. Biased samples can mislead decisions. Use the complement results to see what happens outside the condition. Use lift to compare the conditional chance against the base chance of A.

Practical Applications

Teachers can review pass rates after attendance thresholds. Analysts can study purchase chances after newsletter opens. Health researchers can compare symptoms after exposure groups. Manufacturers can inspect defect rates after stress tests. The same formula supports each case. The key is defining events carefully. Event A should be the outcome you want to measure. Event B should be the condition already known. Clear definitions make the answer meaningful, repeatable, and easier to explain.

Before sharing results, document every assumption. Record whether values came from counts, percentages, or modeled estimates. This habit protects reports from confusion during future reviews and audits too.

FAQs

What is conditional probability?

Conditional probability is the chance of one event occurring after another event is already known. It focuses on a smaller, filtered group instead of the full sample.

What is P(A | B)?

P(A | B) means the probability of Event A given Event B. It equals the overlap of A and B divided by the probability of B.

Can I use raw counts?

Yes. Choose count mode, then enter total observations, Event A count, Event B count, and the count where both events occur.

Can I use percentages?

Yes. Choose probability mode and set the scale to percent. Then enter values like 45, 60, and 37.5 instead of decimals.

Why is P(B) important?

P(B) is the denominator in P(A | B). If P(B) is zero, the condition has no possible cases, so the result is undefined.

What does lift mean?

Lift compares P(A | B) with the base probability of A. A lift above 1 means A is more likely when B is known.

Does conditional probability prove cause?

No. It shows association under a condition. Causation needs stronger study design, controls, and subject knowledge beyond this calculation.

Why export CSV or PDF?

CSV helps with spreadsheets and further analysis. PDF is useful for sharing a simple report with the main result and supporting metrics.