ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Binomial Probability Using Python

Updated on June 28, 2020
Gurpreet Seehra profile image

I enjoy programming. I really like the applications of programming in areas of finance and Operations.

Questions Answered

We discuss in brief what is a binomial event, how binomial probability works and then go on to program binomial probability in Python. We will also solve the following interesting binomial problem.

Problem: The ratio of boys to girls for babies born in a country is 1.09:1. What proportion of its families with exactly 6 children will have at least 3 boys?

Assumption: There are only 2 possible genders.

Binomial Event (Bernoulli Trial)

A binomial event is a statistical experiment that has the following properties:

  • The experiment consists of n repeated trials. e.g. 10 throws of a coin.
  • The trials are independent of each other. e.g. Current outcome doesn't affect the next
  • The outcome of each trial is either success () or failure (). o.r. Head or Tail.
  • Probability of success of 1 trial is p and that of failure is 1-p. i.e. total probability is 1.

Ingredients for Coding in Python

We need:

  1. from statistics Import math to call builtin factorial function.
  2. Write a function for calculating the binomial distribution
  3. That's it.

Python Code

# Import stat module for factorial
from statistics import math

# Define function to get binomial distribution. 
# Here x in the number of successful outcomes
# n is number of trials
# p is probability of success.
# example:binom_dist(2, 5, 1.09) gives probability of 2 boys
# in a family of 5 in a country where
# male to female ratio at birth is 1.09:1
def binom_dist(x, n, p):    
 success_prob = 0
 success_prob
 =(math.factorial(n)/(math.factorial(x)*math.factorial(n-x)))*(p**x)*((1-p)**(n-x))    
    return boys

Using this code to solve problems

Building on the child birth example. Let's assume that male:female ratio is 1.1.

Problem1: What is the probability that a family of 2 has exactly 1 boy and 1 girl.

print(binom_dist(1,2,1.1))

output: 0.773

Problem2: What is the probability that a family of 6 has at least 3 girls.

This is a little tricky one. At least 3 girls means cases where girls' number is 3,4,5 &6. Now, we need to calculate cumulative probability.

# Since we need prob at multiple points we have to loop it in
# We declare a cum_prob variable
# We use 1/1.1 as prob of success as we are using it for girls
# 
n=6
p=1/1.1
cum_prob=0
for i in range(3,n+1,1):    
    cum_prob+=run_binom(i, n, p)

print(cum_prob)
#output: 0.611

Bare code

from statistics import math

def binom_dist(x, n, p):
    boys = 0
    boys =(math.factorial(n)/(math.factorial(x)*math.factorial(n-x)))*(p**x)*((1-p)**(n-x))
    return boys

#Problem1: What is the probability that a family of 2 has exactly 1 boy and 1 girl.

print(binom_dist(1,2,1.1))

#output: 0.773

#Problem2: What is the probability that a family of 6 has at least 3 girls.

# Since we need prob at multiple points we have to loop it in
# We declare a cum_prob variable
# We use 1/1.1 as prob of success as we are using it for girls
# 
n=6
p=1/1.1
cum_prob=0
for i in range(3,n+1,1):    
    cum_prob+=run_binom(i, n, p)

print(cum_prob)
#output: 0.611

Comments

    0 of 8192 characters used
    Post Comment

    No comments yet.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://corp.maven.io/privacy-policy

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)