1. What is Probability of Failure?

The Probability of Failure is the complement of the Probability of Success in probability theory. It represents the likelihood that a particular event will not occur, given the probability that it will occur.

2. How Does the Calculator Work?

The calculator uses the simple formula:

Where:

• \( P_{failure} \) — Probability of failure (0 to 1)
• \( P_{success} \) — Probability of success (0 to 1)

Explanation: The probability of failure is simply 1 minus the probability of success, as these are complementary events.

3. Importance of Probability Calculation

Details: Calculating the probability of failure is essential in risk assessment, reliability engineering, and decision-making processes across various fields including engineering, finance, and quality control.

4. Using the Calculator

Tips: Enter the probability of success as a value between 0 and 1. The calculator will automatically compute the complementary probability of failure.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between P_success and P_failure?
A: They are complementary probabilities that always sum to 1 (P_success + P_failure = 1).

Q2: Can P_success be greater than 1?
A: No, probabilities must be between 0 and 1, inclusive. Values outside this range are invalid.

Q3: What does a P_failure of 0.5 mean?
A: It means there's a 50% chance the event will not occur (and consequently a 50% chance it will occur).

Q4: How is this different from odds of failure?
A: Probability ranges from 0 to 1, while odds are expressed as a ratio (e.g., 1:3 for a probability of 0.25).

Q5: Can this be used for multiple independent events?
A: For multiple independent events, you would need to calculate joint probabilities using multiplication rules.