EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 250+ Courses All in One Bundle
  • Login
Home Finance Finance Resources Finance Formula Binomial Distribution Formula
Secondary Sidebar
Finance Blog
  • Finance Formula
    • Skewness Formula
    • Fixed Asset Turnover Ratio Formula
    • Forecasting Formula
    • EBITDA Margin Formula
    • Accounting Ratio Formula
    • Deferred Annuity Formula
    • Capital Investment Formula
    • Ratio Analysis Formula
    • Loss Ratio Formula
    • Benefit-Cost Ratio Formula
    • Probability Distribution Formula
    • Cash Conversion Cycle Formula
    • Accrued Income
    • DCF Excel summary
    • Price to Earning Ratio Formula
    • Current Yield of Bond Formula
    • Earnings Per Share Formula
    • Manufacturing Overhead Formula
    • FCFF Formula
    • Predetermined Overhead Rate Formula
    • Times Interest Earned Ratio Formula
    • Bank Efficiency Ratio Formula
    • Capital Expenditure Formula
    • Expense Ratio Formula
    • WACC Formula
    • Activity Ratio Formula
    • Standard Error Formula
    • Forward Rate Formula
    • Gearing Formula
    • Prime Cost Formula
    • Productivity Formula
    • t-Test Formula
    • Risk Free Rate Formula
    • Tax Shield Formula
    • Sortino Ratio
    • Reserve Ratio Formula
    • Bond Formula
    • Annualized Rate of Return Formula
    • Conditional Probability Formula
    • Financing Formula
    • Future Value of an Annuity Formula
    • For Profit vs Non Profit
    • Deadweight Loss Formula
    • Inflation Formula
    • Amortized Loan Formula
    • Horizontal Analysis Formula
    • Marginal Utility Formula
    • Kurtosis Formula
    • Macaulay Duration Formula
    • Multiplier Formula
    • Modified Duration Formula
    • Operating Leverage Formula
    • Payout Ratio Formula
    • Statistics Formula
    • Sampling Error Formula
    • Trend Analysis Formula
    • Taylor Rule Formula
    • Put Call Parity Formula
    • Annual Return Formula
    • Discount Rate Formula
    • Cash Flow Formula
    • Dilution Formula
    • Attrition Formula
    • Operating Expense Formula
    • Interpolation Formula
    • Annuity Due Formula
    • Bond Yield Formula
    • Turnover Ratio Formula
    • Efficiency Formula
    • Revenue Per Employee
    • Regression Line Formula
    • Yield to Maturity
    • Pearson Correlation Coefficient Formula
    • Accounting Formula
    • Fiscal Deficit Formula
    • Tax Multiplier Formula
    • Efficiency Ratio Formula
    • Demand Elasticity Formula
    • Gross Margin Formula
    • Elasticity Formula
    • Marginal Benefit Formula
    • Depreciation Formula
    • Cost-Benefit Analysis Formula
    • Percentage Change Formula
    • Levered Beta Formula
    • Shares Outstanding Formula
    • Capital Gain Formula
    • Convexity Formula
    • Gross Income Formula
    • Net Exports Formula
    • Producer Surplus Formula
    • Accounting Rate of Return Formula
    • Net Cash Flow Formula
    • Labor Force Participation Rate Formula
    • Moving Average Formula
    • Net Worth Formula
    • Accounting Profit Formula
    • Disposable Income Formula
    • Discount Formula
    • Average Variable Cost Formula
    • Total Variable Cost Formula
    • Product Cost Formula
    • Marginal Product Formula
    • Break-Even Sales Formula
    • Return on Sales Formula
    • Cost of Goods Manufactured Formula
    • Average Fixed Cost Formula
    • Stock Turnover Ratio Formula
    • Operating Ratio Formula
    • Equity Ratio Formula
    • Net Present Value Formula
    • Aggregate Demand Formula
    • Volatility Formula
    • Marginal Product of Labor Formula
    • Z Test Statistics Formula
    • Standard Cost Formula
    • Velocity of Money Formula
    • Invested Capital Formula
    • Unlevered Beta Formula
    • Bank Reconciliation Formula
    • Portfolio Return Formula
    • Central Tendency Formula
    • Accumulated Depreciation Formula
    • Intrinsic Value Formula
    • Decile Formula
    • Vector Cross Product Formula
    • Effective Annual Rate Formula
    • CAGR Formula
    • Mode Formula
    • Arithmetic Mean Formula
    • Real GDP Formula
    • Gini Coefficient Formula
    • Expected Value Formula
    • Price Elasticity of Supply Formula
    • Net Operating Income Formula
    • Profit Percentage Formula
    • GDP Per Capita Formula
    • Altman Z Score
    • Quartile Deviation Formula
    • Return on Capital Employed Formula
    • Consumer Price Index Formula
    • Economic Profit Formula
    • Market Share Formula
    • Real Interest Rate Formula
    • Income Elasticity of Demand Formula
    • Income From Operations Formula
    • Indexation Formula
    • Sales Formula
    • Money Multiplier Formula
    • GDP Deflator Formula
    • Residual Income Formula
    • Effective Interest Rate Formula
    • Coupon Bond Formula
    • Current Account Formula
    • Total Cost Formula
    • Total Expense Ratio Formula
    • Net Sales Formula
    • Percentage Decrease Formula
    • Uncertainty Formula
    • Nominal GDP Formula
    • Effect Size Formula
    • Delta Formula
    • Cost of Sales Formula
    • Fixed Cost Formula
    • Unemployment Rate Formula
    • Present Value of Annuity Formula
    • Compounding Formula
    • Geometric Distribution Formula
    • National Income Formula
    • Accounts Receivables Turnover Formula
    • Integer Formula
    • Ending Inventory Formula
    • Owner's Equity Formula
    • Capacity Utilization Rate Formula
    • Interest Formula
    • Nominal Interest Rate Formula
    • Risk Premium Formula
    • Interest Coverage Ratio Formula
    • Gross Profit Margin Formula
    • Diluted EPS Formula
    • Return On Average Equity Formula
    • Return on Average Assets Formula
    • Working Capital Formula
    • Revenue Per Employee Ratio Formula
    • Capital Employed Formula
    • Rule of 72 Formula
    • Inventory Turnover Ratio Formula
    • Preferred Dividend Formula
    • Retention Ratio Formula
    • Present Value Factor Formula
    • Equity Multiplier Formula
    • Continuous Compounding Formula
    • Return on Assets (ROA) Formula
    • Portfolio Variance Formula
    • Weighted Average Formula
    • Net Working Capital Formula
    • Tax Equivalent Yield Formula
    • Poisson Distribution Formula
    • Current Ratio Formula
    • Debt Ratio Formula
    • Quick Ratio Formula
    • Payback Period Formula
    • Marginal Cost Formula
    • Debt to Income Ratio Formula
    • Book Value Per Share Formula
    • Asset Turnover Ratio Formula
    • Perpetuity Formula
    • Bid-Ask Spread Formula
    • Price to Book Value Formula
    • Capital Gains Yield Formula
    • Net Profit Margin Formula
    • DuPont Formula
    • Bond Pricing Formula
    • Binomial Distribution Formula
    • Sustainable Growth Rate Formula
    • Average Collection Period Formula
    • Net Income Formula
    • CAPM Formula
    • Cost of Goods Sold Formula
    • Economic Order Quantity (EOQ) Formula
    • Amortization Formula
    • Enterprise Value Formula
    • Beta Formula
    • Cost of Equity Formula
    • Rate of Return Formula
    • Revenue Formula
    • Markup Price Formula
    • Cash Flow from Operations Formula
    • Simple Interest Rate Formula
    • Consumer Surplus Formula
    • Asset to Sales Ratio Formula
    • Debt Service Coverage Ratio Formula
    • Capitalization Rate Formula
    • Cost of Debt Formula
    • Straight Line Depreciation Formula
    • Variable Costing Formula
    • Return on Invested Capital Formula
    • Profitability Index Formula
    • Expected Return Formula
    • Cost of Capital Formula
    • Price Index Formula
    • Average Total Cost Formula
    • Discount Factor Formula
    • Price Elasticity Formula
    • Profitability Ratios Formula
    • Financial Leverage Formula
    • Contribution Margin Formula
    • Time Value of Money Formula
    • Balance Sheet Formula
    • Opportunity Cost Formula
    • Current Assets Formula
    • Operating Cycle Formula
    • Operating Margin Formula
    • Bond Equivalent Yield Formula
    • Marginal Revenue Formula
    • Sales Revenue Formula
    • Net Debt Formula
    • Times Interest Earned Formula
    • Gordon Growth Model Formula
    • Required Rate of Return Formula
    • Break Even Analysis Formula
    • Inventory Formula
    • Marginal Propensity to Consume Formula
    • Debt to Asset Ratio Formula
    • Solvency Ratio Formula
    • Interest Expense Formula
    • Leverage Ratio Formula
    • Dividend Payout Ratio Formula
    • Operating Profit Margin Formula
    • PEG Ratio Formula
    • Net Interest Margin Formula
    • Return on Equity (ROE) Formula
    • Overhead Ratio Formula
    • Future Value Formula
    • Days in Inventory Formula
    • Market Capitalization Formula
    • Sharpe Ratio Formula
    • Cash Ratio Formula
    • Retained Earnings Formula
    • Average Rate of Return Formula
    • Current Liabilities Formula
    • Equity Value Formula
    • Relative Risk Reduction Formula
    • Capital Adequacy Ratio Formula
    • Debtor Days Formula
    • DPMO Formula
    • Average Formula
    • Exponential Growth Formula
    • Net Realizable Value Formula
    • Range Formula
    • Shareholders' Equity Formula
    • Sinking Fund Formula
    • Doubling Time Formula
    • Salvage Value Formula
    • Coupon Rate Formula
    • Simple Interest Formula
    • Correlation Formula
    • R - Squared Formula
    • MTBF Formula
    • Change in Net Working Capital Formula
    • Midrange Formula
    • Normal Distribution Formula
    • Mean Formula
    • Population Mean Formula
    • Median Formula
    • Central Limit Theorem Formula
    • Free Cash Flow Formula
    • Stockholder's Equity Formula
    • Acid-Test Ratio Formula
    • Percentile Rank Formula
    • Purchasing Power Parity Formula
    • Harmonic Mean Formula
    • Relative Standard Deviation Formula
    • T Distribution Formula
    • Normalization Formula
    • Operating Income Formula
    • Markup Percentage Formula
    • Relative Change Formula
    • Maturity Value Formula
    • Salary Formula
    • High Low Method
    • Income Statement Formula
    • Market to Book Ratio Formula
    • Dividends Per Share Formula
    • Daily Compound Interest Formula
    • Working Capital Turnover Ratio Formula
    • Weighted Mean Formula
    • Compounded Annual Growth Rate Formula
    • Regression Formula
    • Margin of Error Formula
    • Hypergeometric Distribution Formula
    • Standard Normal Distribution Formula
    • NOPAT Formula
    • Effective Tax Rate Formula
    • Degree of Operating Leverage Formula
    • Outliers Formula
    • Information Ratio Formula
    • Percent Error Formula
    • Hypothesis Testing Formula
    • Activity Based Costing Formula
    • Coverage Ratio Formula
    • Market Risk Premium Formula
    • Degree of Financial Leverage Formula
    • Absorption Costing Formula
    • Future Value of Annuity Due Formula
    • Internal Growth Rate Formula
    • F-Test Formula
    • Covariance Formula
    • Population Variance Formula
    • Coefficient of Determination Formula
    • Adjusted R Squared Formula
    • Compound Interest Formula
    • Gross Profit Formula
    • Accounting Equation Formula
    • Sample Size Formula
    • Sample Standard Deviation Formula
    • Quartile Formula
    • Variance Analysis Formula
    • Correlation Coefficient Formula
    • Z Score Formula
    • Variance Formula
    • Present Value Formula
    • Coefficient of Variation Formula
    • Net Asset Value Formula
    • Profit Margin Formula
    • Holding Period Return Formula
    • Capital Asset Pricing Model Formula
    • Present Value of Annuity Due Formula
    • Depreciation Expenses Formula
    • Annuity Formula
    • Taxable Income Formula
    • Profit Formula
    • Monthly Compound Interest Formula
    • Equity Formula
    • Return on Total Assets Formula
    • Alpha Formula
    • Debt to Equity Ratio Formula
    • EBITDA Formula
    • Accrued Interest Formula
    • Dividend Formula
    • Common Stock Formula
    • Mortgage Formula
    • Growth Rate Formula
    • Absolute Value Formula
  • Accounting fundamentals (700+)
  • Asset Management Tutorial (200+)
  • Banking (44+)
  • Corporate Finance Basics (373+)
  • Credit Research Fundamentals (6+)
  • Economics (88+)
  • Financial Modeling in Excel (17+)
  • Investment Banking Basics (140+)
  • Investment Banking Careers (29+)
  • Trading for dummies (69+)
  • valuation basics (27+)
  • Insurance Resources (14+)
  • Top Finance Books (7+)
Finance Blog Courses
  • Investment Banking Course
  • Investment Banking Online Course
  • Financial Modeling Certification

Binomial Distribution Formula

By Madhuri ThakurMadhuri Thakur

Binomial Distribution Formula

Binomial Distribution Formula (Table of Contents)

  • Formula
  • Calculator
  • Examples With Excel Template

What is Binomial Distribution Formula?

The binomial distribution is the probability distribution formula that summarizes the likelihood of an event occurs either A win, B loses or vice-versa under given set parameters or assumptions. However, there is an underlying assumption of the binomial distribution where there is only one outcome is possible for each trial, either success or loss. And each trial in itself is mutually exclusive from another one.

Suppose, if we have defined one outcome out of two is defined as a success, then the probability of x successes out of N trials can be computed as:

P(X) = nCx * px * (1 – p)(n-x)
P(X) = (n! / (x! * (n – x)!)) * px * (1 – p)(n-x)

Where p is the probability of success on one trial.

Start Your Free Investment Banking Course

Download Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

Examples of Binomial Distribution Formula

Let’s take an example to understand the calculation of Binomial Distribution in a better manner.

You can download this Binomial Distribution Formula Excel Template here – Binomial Distribution Formula Excel Template

Binomial Distribution Formula – Example #1

A coin is flipped 10 times. Calculate the probability of getting 5 heads using a Binomial distribution formula.

Example 1-1

Solution:

Probability is calculated using the binomial distribution formula as given below.

P(X) = (n! / (x! * (n – x)!)) * px * (1 – p)(n-x)

Binomial Distribution Formula Example 1-2

  • P(x=5) = (10! / (5! * (10 – 5)!)) * (0.5)^5 * (1 – 0.5)^(10 – 5)
  • P(x=5) = (10! / (5! * 5!)) * (0.5)^5 * (0.5)^5
  • P(x=5) = 0.2461

The probability of getting exactly 5 successes is 0.2461

Binomial Distribution Formula – Example #2

In a study, it is found that 70% of people who purchase pet insurance are mostly women. If we randomly select 9 pet insurance owners. What is the probability, out of the 7 will be women?

Example 2-1

Solution:

Probability is calculated using the binomial distribution formula as given below.

P(X) = (n! / (x! * (n – x)!)) * px * (1 – p)(n-x)

 Binomial Distribution Formula Example 2-2

  • P(x=7) = (9! / (7! * (9 – 7)!)) * (0.7)^7 * (1 – 0.7)^(9 – 7)
  • P(x=7) = (9! / (7! * 2!)) * (0.7)^7 * (0.3)^2
  • P(x=7) = 0.2668

Binomial Distribution Formula – Example #3

Last year in the survey of Autocar India, it was found that 70% of buyers of sports cars are men. If 10 sports car owners are randomly selected. What is the probability, out of the 6 will be men?

Example 3-1

Solution:

Probability is calculated using the binomial distribution formula as given below.

P(X) = (n! / (x! * (n – x)!)) * px * (1 – p)(n-x)

Binomial Distribution Formula Example 3-2

  • P(x=5) = (10! / (6! * (10 – 6)!)) * (0.7)^6 * (1 – 0.7)^(10 – 6)
  • P(x=5) = (10! / (6! * 4!)) * (0.7)^6 * (0.3)^4
  • P(x=5) = 0.2001

Explanation

A binomial distribution basically depends much more on the number of trials or observations are done. While each trial defines its own probability of outcome value or, in other words. A binomial random variable defines as a successful outcome of x in n number of the repeated trial of a binomial experiment. While a binomial random variable’s probability distribution is also known as a binomial distribution.

If we take an example, when we toss a coin, the probability of obtaining a head is 0.5 of 50% out of 100%. If we perform 100 trials. The expected value of obtaining heads is 50(100 x 0.5). The binomial distribution is a statistical term to predict the outcome of an event to occur, like what is the probability of a sportsman to win in the competition.

There are certain steps and rules to meet the specific criteria of Binomial Distribution models in order to use the formula.

Step 1: Fixed Trials

In this course of action, there is a certain set of a fixed number of trials which can’t be altered in the course of the whole process. The number of trials in the binomial probability formula is represented by the letter “n”. In our case, flips a coin, free throws, wheel spins are the fixed number of trials.

Step 2: Independent Trials

Independent Trial is another condition of a binomial probability in which trials are independent of each other where the outcome of one trial doesn’t impact much more on the subsequent trials.

If we take an example where independent trials, maybe tossing a coin or rolling dice, is independent of the subsequent events.

Step 3: Fixed Probability of Success

In this type of distribution, the probability of getting success remain the same for all trials. For example, if we toss a coin, the probability of an outcome of every event, either head or tail, is 0.5 since there are two possible outcomes.

Step 4: Two Mutually exclusive Outcomes

In this distribution, there are only two types of mutually exclusive outcomes that exist, either success or failure. Where success has been defined in a positive term. The purpose of the trial is to validate what we have defined as a success. Either it is positive or negative.

Relevance and Uses of Binomial Distribution Formula

The binomial distribution model is the most important probability model; it is required when there are two possible outcomes expected. It came into existence when there were more than two distinct outcomes. In that case, a multinomial probability is more appropriate. But here, our major concern is more on the situation where the outcome is dichotomous.

The use of the binomial distribution requires three models:

  • Each outcome of the process results in the one or two outcomes, either success or failure.
  • The outcome of each process results in the same probability.
  • Each outcome is mutually exclusive to the other of the process.

Binomial Distribution Formula Calculator

You can use the following Binomial Distribution Calculator.

n
p
x
Binomial Distribution Formula
 

Binomial Distribution Formula = [n ! / x ! * (n - x) !] * px * (1 - p)n - x
[0! / 0! * (0 - 0)!] * 00 * (1 -0)0-0 = 0

Binomial Distribution Formula in Excel (With Excel Template)

Here we will do another example of the Binomial Distribution in Excel. It is very easy and simple.

Calculate the Binomial Distribution in Excel using function BINOM.DIST.

Below is the Syntax of Binomial Distribution formula in Excel.

Synatx of Binomial Distribution

Where the Binomial distribution uses the following argument:

  • Number_s: Defines the number of success in the trial.
  • Trials: Number of independent trials.
  • Probabiity_s: Success probability in each trial.
  • Cumulative: Allows to pick logical value either True or False.

Binomial Distribution Formula Example 4-1

Probability is calculated using the binomial distribution formula is calculated as:

Binomial Distribution Formula Example 4-2

Recommended Articles

This has been a guide to Binomial Distribution Formula. Here we discuss how to calculate Binomial Distribution along with practical examples. We also provide a Binomial Distribution calculator with a downloadable excel template. You may also look at the following articles to learn more –

  1. The formula for Central Limit Theorem
  2. Standard Normal Distribution Formula
  3. Calculation of Normal Distribution
  4. Formula for T Distribution Formula
Popular Course in this category
All in One Financial Analyst Bundle- 250+ Courses, 40+ Projects
  250+ Online Courses |  1000+ Hours |  Verifiable Certificates |  Lifetime Access
4.9
Price

View Course

Related Courses

Investment Banking Course (123 Courses, 25+ Projects)4.9
Investment Banking Course (123 Courses, 25+ Projects)4.8
Financial Modeling Course (7 Courses, 14 Projects)4.7
0 Shares
Share
Tweet
Share
Primary Sidebar
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Investment Banking Jobs Offer
  • Finance Formula
  • All Tutorials
Certification Courses
  • All Courses
  • Financial Analyst All in One Bundle
  • Investment Banking Training
  • Financial Modeling Course
  • Equity Research Course
  • Private Equity Training Course
  • Business Valuation Course
  • Mergers and Acquisitions Course

ISO 10004:2018 & ISO 9001:2015 Certified

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Financial Modeling Course

3 Statement Model Creation, Revenue Forecasting, Supporting Schedule Building, & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Investment Banking Course

Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA

Download Binomial Distribution Formula Excel Template

EDUCBA

डाउनलोड Binomial Distribution Formula Excel Template

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more