Union Probability Calculator Formula

Understand the math behind the union probability calculator. Each variable explained with a worked example.

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Formulas Used

P(A or B)

p_union = p_a + p_b - p_a_and_b

P(A or B) as %

p_union_pct = (p_a + p_b - p_a_and_b) * 100

P(Neither)

p_neither = 1 - (p_a + p_b - p_a_and_b)

Variables

VariableDescriptionDefault
p_aP(A)0.3
p_bP(B)0.5
p_a_and_bP(A and B)0.1

How It Works

How to Calculate Union Probability

Formula

P(A or B) = P(A) + P(B) - P(A and B)

The addition rule accounts for the overlap between events A and B. If you simply add P(A) and P(B), the intersection is counted twice, so you subtract P(A and B) once. For mutually exclusive events, P(A and B) = 0.

Worked Example

P(A) = 0.3, P(B) = 0.5, P(A and B) = 0.1. Find P(A or B).

p_a = 0.3p_b = 0.5p_a_and_b = 0.1
  1. 01P(A or B) = P(A) + P(B) - P(A and B)
  2. 02P(A or B) = 0.3 + 0.5 - 0.1
  3. 03P(A or B) = 0.7
  4. 04P(Neither) = 1 - 0.7 = 0.3

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