Sample Probability Calculator

Sample Probability Calculator calculator can be used to calculate the probability of getting exactly \( k \) successes in \( n \) independent Bernoulli trials with probability of success \( p \) in each trial.

Input Parameters

Calculation Results

Calculation Formula

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- C(n, k) is the binomial coefficient: n! / (k! * (n-k)!)
- p is the probability of success
- (1-p) is the probability of failure

Result

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Sample Probability Calculator Calculator Usage Guide

Learn how to use the Sample Probability Calculator calculator and its working principles

How to Use the Calculator

  1. Enter the number of trials \( n \) (the total number of independent events)
  2. Enter the number of successes \( k \) (the specific number of successful events you want to find the probability for)
  3. Enter the probability of success \( p \) for each trial (a value between 0 and 1)
  4. Click the "Calculate" button to compute the probability
  5. The result will be displayed in the Result section

Example

Suppose you want to calculate the probability of getting exactly 3 heads when flipping a fair coin 5 times:

  • n = 5 (number of coin flips)
  • k = 3 (number of heads)
  • p = 0.5 (probability of getting heads in each flip)

After entering these values and clicking "Calculate", the probability will be displayed as the result.

Working Principle

This calculator uses the binomial probability formula to calculate the probability of getting exactly \( k \) successes in \( n \) independent Bernoulli trials. The formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

  • C(n, k) is the binomial coefficient, representing the number of ways to choose k successes from n trials
  • p is the probability of success in each trial
  • (1-p) is the probability of failure in each trial