Probability

Binomial Probability Formula - Probability

Learn the binomial probability formula with examples, step-by-step guide, and calculator tools. Calculate probability of k successes in n independent trials

The binomial probability formula is a fundamental concept in probability. Calculate probability of k successes in n independent trials. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

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

Variables

P(X=k)
Probability of exactly k successes
n
Number of trials
k
Number of successes
p
Probability of success

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [10,3,0.5] → P(X=3) = C(10,3) × 0.5³ × 0.5⁷ = 0.117

Example 2

Example 2: 0.117

Frequently Asked Questions

What is the binomial probability formula?

Calculate probability of k successes in n independent trials

How do I calculate binomial probability formula?

Use the formula: P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}. Follow the steps provided above.

What tools can help with binomial probability formula?

We provide online calculators: binomial-probability-calculator

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