1. What is the Consecutive Probability Formula?

The consecutive probability formula calculates the probability of an event occurring at least once over multiple independent attempts. It's useful in scenarios like repeated trials, risk assessment, and probability modeling.

2. How Does the Calculator Work?

The calculator uses the consecutive probability formula:

Where:

• \( p_{single} \) — Probability of event occurring in a single attempt (0 to 1)
• \( n \) — Number of attempts
• \( p \) — Probability of event occurring at least once in n attempts

Explanation: The formula calculates the complement probability (event not happening in all attempts) and subtracts it from 1 to get the probability of it happening at least once.

3. Practical Applications

Details: This calculation is used in quality control (probability of defect over multiple items), risk assessment (probability of failure over time), gaming (drop rates over multiple attempts), and scientific research.

4. Using the Calculator

Tips: Enter the single-attempt probability (between 0 and 1) and the number of attempts (positive integer). The calculator will compute the cumulative probability.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for dependent events?
A: No, this formula assumes independent attempts where the probability doesn't change between attempts.

Q2: What if my probability per attempt is very small?
A: For very small p_single and large n, the formula approximates to p ≈ n × p_single.

Q3: Can I use percentages instead of decimals?
A: Yes, just divide your percentage by 100 before entering (e.g., 5% = 0.05).

Q4: How accurate is this calculation?
A: Mathematically exact for independent events with constant probability.

Q5: What's the difference between consecutive and cumulative probability?
A: In this context, they're the same - the probability of at least one occurrence over multiple attempts.