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Addition Rule Of Probability Calculator

Work out addition rule of probability instantly with clear inputs, formula shown and shareable results.

About Addition Rule Of Probability Calculator

The general addition rule is P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Subtracting the intersection removes the double counting of outcomes belonging to both events.

Formula

Addition rule

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Worked example

With the default values below, Addition Rule Of Probability Calculator returns P(A or B) of 0.70000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Probability of Aaccepts 0–100 %
50 %
Probability of Baccepts 0–100 %
40 %
Probability of bothaccepts 0–100 %
20 %

Results

P(A or B)
0.70000000
P(exactly one)
0.50000000
P(neither)
0.30000000
P(A)·P(B) — equals P(both) only if independent
0.20000000

Step by step

  1. 1Values used
  2. 2Addition rule
  3. 3P(A or B)= 0.70000000
  4. 4P(exactly one)= 0.50000000
  5. 5P(neither)= 0.30000000
  6. 6P(A)·P(B) — equals P(both) only if independent= 0.20000000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 0.5, 0.4 and an overlap of 0.2?

The union is 0.7, exactly one occurs with probability 0.5, and neither with 0.3.

Are these events independent?

No. P(A)P(B) = 0.2 happens to equal P(both) here, so in this case they are independent.

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