1. What is Probability of Failure?

The probability of failure is the complement of the probability of success in a binary outcome scenario. It represents the likelihood that an event will not occur, given the probability that it will occur.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( p_{success} \) — Probability of success (between 0 and 1)
• \( p_{failure} \) — Probability of failure (between 0 and 1)

Explanation: Since success and failure are mutually exclusive and exhaustive outcomes, their probabilities must sum to 1.

3. Importance of Probability Calculation

Details: Calculating failure probability is fundamental in reliability engineering, risk assessment, and decision-making processes where understanding both possible outcomes is crucial.

4. Using the Calculator

Tips: Enter the probability of success as a value between 0 and 1 (e.g., 0.75 for 75% chance). The calculator will compute the complementary probability of failure.

5. Frequently Asked Questions (FAQ)

Q1: What if my probability of success is 0?
A: A success probability of 0 means failure is certain (probability = 1).

Q2: What if my probability of success is 1?
A: A success probability of 1 means failure is impossible (probability = 0).

Q3: Can I enter percentages instead of decimals?
A: No, you must convert percentages to decimals (e.g., 25% = 0.25).

Q4: What are some practical applications?
A: Used in reliability testing, quality control, financial risk assessment, and any scenario with binary outcomes.

Q5: How does this relate to probability distributions?
A: This is the simplest case of a Bernoulli distribution where there are only two possible outcomes.