Math & Statistics

Probability Calculator

Calculate the combined probability of two independent events.

Enter the probability of two independent events to calculate the probability of both happening (AND) or at least one happening (OR).

Enter a value between 0 and 100.
Enter a value between 0 and 100.

Results (assuming independent events)

P(A and B)

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P(A or B)

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How to Use This Tool

  1. Enter the probability of Event A as a percentage.
  2. Enter the probability of Event B as a percentage.
  3. Click Calculate to see the combined AND and OR probabilities.

Probability Formulas for Independent Events

P(A and B) = P(A) × P(B)

P(A or B) = P(A) + P(B) − P(A and B)

What "Independent Events" Means

Two events are independent when the outcome of one doesn't affect the probability of the other — like flipping a coin and rolling a die. This calculator assumes independence; for dependent events (where one outcome affects the other), different formulas involving conditional probability would apply.

Why We Subtract P(A and B) for "OR"

Simply adding P(A) + P(B) would double-count the overlap where both events happen — subtracting P(A and B) corrects for this overlap, ensuring the combined probability doesn't exceed 100%.

Frequently Asked Questions

Does this work for dependent events?

No, this calculator assumes the two events are independent (one doesn't affect the other's probability). Dependent events require conditional probability formulas that account for how one event influences the other.

Why is P(A or B) not just P(A) + P(B)?

Simply adding the two would double-count the scenario where both events happen simultaneously — subtracting P(A and B) corrects for this overlap.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.