Probability of Success After N Trials Calculator

How to Use This Calculator

1. Enter the number of trials (N) you plan to conduct. This is the total number of independent attempts.
2. Enter the probability of success (p) for each individual trial. This should be a number between 0 and 1, where 0 means no chance of success and 1 means certain success.
3. Click the "Calculate" button to compute the probability of achieving at least one success in all N trials.
4. The result will show the probability of at least one success occurring in the N trials.

Understanding the Formula

The calculator uses the complement probability formula:

P(at least 1 success) = 1 - (1-p)^N

This formula works because:

• The probability of failing a single trial is (1-p)
• The probability of failing all N trials in a row is (1-p)^N
• Therefore, the probability of at least one success is 1 minus the probability of no successes

Example Usage

Suppose you're rolling a fair die (6 sides) 3 times (N=3) and want to find the probability of rolling at least one 6:

1. N = 3 (number of trials)
2. p = 1/6 = 0.1667 (probability of rolling a 6 on any single roll)
3. Calculate: P(at least 1 success) = 1 - (1-1/6)³ = 1 - (5/6)³ ≈ 0.4213

So there's approximately a 42.13% chance of rolling at least one 6 in 3 rolls.