1. What is Probability of Success After N Trials?

Definition: This calculator determines the probability of at least one success occurring in a series of independent trials.

Purpose: It helps in statistical analysis, risk assessment, and probability modeling across various fields including science, engineering, and finance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Probability of at least one success (0 to 1)
• \( p \) — Probability of success per trial (0 to 1)
• \( n \) — Number of independent trials (≥1)

Explanation: The formula calculates the complement probability (all trials failing) and subtracts it from 1 to get the probability of at least one success.

3. Importance of This Calculation

Details: Understanding cumulative probability helps in decision making, quality control, experimental design, and risk management.

4. Using the Calculator

Tips: Enter the probability per trial (between 0 and 1) and the number of trials (1 or more). The result shows the probability of at least one success occurring.

5. Frequently Asked Questions (FAQ)

Q1: What if my probability per trial is 0?
A: The result will always be 0 since success is impossible in every trial.

Q2: What if my probability per trial is 1?
A: The result will always be 1 since success is guaranteed in every trial.

Q3: How does increasing trials affect the probability?
A: More trials increase the chance of at least one success, approaching 1 as n increases.

Q4: Can I use percentages instead of decimals?
A: Convert percentages to decimals (e.g., 20% = 0.20) before entering.

Q5: Does this work for dependent events?
A: No, this formula assumes independent trials with constant probability.