1. What is Probability of Success After N Trials?

Definition: This calculator computes the probability of getting at least one success in multiple independent trials.

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

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 (positive integer)

Explanation: The formula calculates the complement of the probability of all trials failing.

3. Importance of Probability Calculation

Details: Understanding cumulative probabilities helps in decision making, experimental design, and risk evaluation.

4. Using the Calculator

Tips: Enter the probability per trial (0 to 1) and number of trials (positive integer). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What does "at least one success" mean?
A: It means one or more successes in all trials (1, 2, ..., up to n successes).

Q2: Can I use percentages for probability?
A: Convert percentages to decimals (e.g., 25% = 0.25) before entering.

Q3: Does this assume independent trials?
A: Yes, the formula assumes each trial is independent with constant probability.

Q4: What if I want exactly one success?
A: Use the binomial formula: \( n \times p \times (1-p)^{n-1} \).

Q5: How accurate are the results?
A: Mathematically precise when inputs are accurate, though real-world factors may affect actual outcomes.