Independent Events Calculator Formula

Understand the math behind the independent events calculator. Each variable explained with a worked example.

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Formulas Used

P(A and B)

p_both = p_a * p_b

P(A or B)

p_either = p_a + p_b - p_a * p_b

P(Neither)

p_neither = (1 - p_a) * (1 - p_b)

Variables

VariableDescriptionDefault
p_aP(A)0.5
p_bP(B)0.3

How It Works

How to Calculate Joint Probability of Independent Events

Formula

P(A and B) = P(A) * P(B)

Two events are independent if the occurrence of one does not affect the probability of the other. For independent events, the joint probability is simply the product of the individual probabilities. This extends to any number of events: P(A and B and C) = P(A) * P(B) * P(C).

Worked Example

A coin has P(heads) = 0.5 and a die has P(six) = 0.3 (loaded). What is the probability of both?

p_a = 0.5p_b = 0.3
  1. 01P(A and B) = P(A) * P(B)
  2. 02P(heads and six) = 0.5 * 0.3 = 0.15
  3. 03P(heads or six) = 0.5 + 0.3 - 0.15 = 0.65
  4. 04P(neither) = (1 - 0.5) * (1 - 0.3) = 0.5 * 0.7 = 0.35

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