1. What is a Probability of Success Calculator?

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

Purpose: It helps in statistical analysis, risk assessment, and decision-making processes where repeated trials are involved.

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 of the probability that all trials fail (1 - p)^n, giving the probability that at least one trial succeeds.

3. Importance of Probability Calculation

Details: Understanding cumulative probabilities helps in risk assessment, experimental design, and predicting outcomes in repeated scenarios.

4. Using the Calculator

Tips: Enter the probability per trial (between 0 and 1) and the number of trials (1 or more). The calculator will compute the cumulative probability.

5. Frequently Asked Questions (FAQ)

Q1: What if my probability per trial is 0?
A: If p=0, P will always be 0 regardless of n, as success is impossible.

Q2: What if my probability per trial is 1?
A: If p=1, P will always be 1 for any n≥1, as success is guaranteed.

Q3: How does increasing trials affect the probability?
A: More trials increase P, approaching 1 as n becomes large (for p>0).

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

Q5: Does this assume independent trials?
A: Yes, the formula assumes each trial is independent with constant p.