Probability of Success After N Trials Calculator







Formula

The formula to calculate the probability of success after N trials is:

\[ P(X=k) = C(n, k) \cdot p^k \cdot (1-p)^{(n-k)} \]

Where:

What is Probability Of Success After N Trials?

The Probability of Success After N Trials, often referred to in statistics as the binomial probability, is the likelihood of achieving a specific number of "successes" in a set number of trials or attempts. A "success" is defined as the outcome that we are interested in. This concept is used in binomial experiments where each trial is independent and has only two possible outcomes - success or failure. The probability remains constant throughout all trials.

Example Calculation

Let's assume the following values:

Step 1: Calculate the combinations:

\[ C(10, 3) = \frac{10!}{3!(10-3)!} = 120 \]

Step 2: Calculate the probability of k successes:

\[ P(X=3) = 120 \cdot 0.5^3 \cdot (1-0.5)^{(10-3)} = 0.1172 \]

Therefore, the probability of having exactly 3 successes out of 10 trials is approximately 0.1172.