Enter the sum of probabilities of all observed outcomes into the calculator to determine the defective probability.

Defective Probability Formula

The following formula is used to calculate the defective probability.

DP = 1 - ΣP(Oi)


  • DP is the defective probability
  • ΣP(Oi) is the sum of probabilities of all observed outcomes

To calculate the defective probability, sum up the probabilities of all observed outcomes. Subtract this sum from 1. The result is the defective probability, which represents the probability of outcomes that were not observed or were overlooked.

What is a Defective Probability?

A Defective Probability is a probability measure that does not satisfy the condition that the sum of probabilities of all possible outcomes equals one. This usually occurs when the probability space is not completely defined or some outcomes are ignored or overlooked. It’s called “defective” because it violates one of the fundamental axioms of probability theory.

How to Calculate Defective Probability?

The following steps outline how to calculate the Defective Probability.

  1. First, gather the probabilities of all observed outcomes (P(Oi)).
  2. Next, calculate the sum of all probabilities of observed outcomes (ΣP(Oi)).
  3. Next, subtract the sum of probabilities of observed outcomes from 1 (DP = 1 – ΣP(Oi)).
  4. Finally, calculate the Defective Probability (DP).
  5. After inserting the probabilities and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Probabilities of observed outcomes (P(Oi)):

P(O1) = 0.2

P(O2) = 0.3

P(O3) = 0.1

P(O4) = 0.4