WHAT THIS TOOL DOES

This combined probability calculator works out probability for two events: AND, OR with no overlap, or OR with overlap.

Enter P(A), P(B), and optionally P(A∩B). The inputs accept fractions, decimals or percentages.

Best folder name: combined-probability

HOW TO USE IT

Choose AND when both independent events must happen.

Choose OR no overlap when either event can happen but they cannot happen together.

Choose OR with overlap when the events can both happen, then enter the overlap probability.

Press SOLVE to show the converted values, formula and final probability.

KEY RULES

AND: multiply probabilities when events are independent.

OR no overlap: add probabilities when events cannot both happen.

OR with overlap: add A and B, then subtract the overlap once.

Formula: P(A∪B)=P(A)+P(B)-P(A∩B).

EXAMPLES

AND example: if P(A)=30% and P(B)=25%, independent AND gives 0.30 × 0.25 = 0.075.

OR no overlap example: 20% or 10% gives 30% when the two events cannot overlap.

OR overlap example: 40% + 35% - 10% gives 65% when overlap is counted once.

Use official probability wording to decide which rule applies.

WHO USES IT

Students use it for GCSE maths, probability trees, independent events, mutually exclusive events and Venn diagram questions.

Teachers and tutors use it to show when to multiply, add, or subtract overlap.

It can also help with quick checks for risk, chance, selection and outcome comparisons.

Common searches: combined probability calculator, AND probability calculator, OR probability calculator.

DEVICE HELP

The calculator is split into input and result pages so mobile screens do not crush the buttons or hide the answer.

Extra explanations are split into internal pages to prevent hidden content behind the footer.

Inputs and buttons have accessible labels. Keyboard: Enter solves. Escape resets to the worked example.

Every internal page keeps PREV and NEXT visible.

RELATED PAGES

This page sits after the simple probability calculator and before odds to probability in the probability tools section.

Use the hub for dice probability, coin toss probability, expected value and risk tools.

Internal NEXT loops back to the calculator page.