What is a Binomial Probability Distribution?
A binomial probability distribution describes the likelihood of a given number of successes in a fixed number of trials, where each trial has two possible outcomes: success or failure. It is governed by three parameters:
- Number of Trials (n): The total number of experiments conducted.
- Probability of Success (p): The likelihood of success in a single trial.
- Number of Successes (k): The number of successful outcomes you are analyzing.
The formula for calculating the probability of k successes is:
\[ P(X = k) = \binom{n}{k} p^k (1 – p)^{n-k} \]Where:
- \( n \): Total number of trials
- \( k \): Number of successes
- \( p \): Probability of success in a single trial
The binomial coefficient is calculated as:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \]This formula represents the likelihood of observing exactly \( k \) successes in \( n \) independent trials of a binary experiment (success or failure) where the probability of success is \( p \).
Try this Tools:- Binomial Coefficient Calculator
