{"id":25944,"date":"2015-02-27T10:29:14","date_gmt":"2015-02-27T10:29:14","guid":{"rendered":"http:\/\/vskills.in\/certification\/blog\/?p=25944"},"modified":"2024-04-03T13:15:47","modified_gmt":"2024-04-03T07:45:47","slug":"the-birthday-problem-in-probability-theory","status":"publish","type":"post","link":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/","title":{"rendered":"The Birthday Problem in Probability Theory"},"content":{"rendered":"<p style=\"text-align: center\"><a ref=\"magnificPopup\" href=\"http:\/\/vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-25995\" src=\"http:\/\/vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\" alt=\"The Birthday Problem in Probability Theory\" width=\"259\" height=\"194\" \/><\/a><\/p>\n<p><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\"><span style=\"font-size: medium\">One of the most common birthdays cited in probability theory is the birthday problem where the probability that at least two people in a group of people would have their birthdays on the same day. This means that the month and day of birth is the same, but the year does not have to be the same. This probability increases as the number of people in a group increases, but to find the exact probability for a group comprising a particular number of people, we will have to make certain assumptions. We assume that whoever is born on the 29<\/span><sup><span style=\"font-size: small\">th<\/span><\/sup><span style=\"font-size: medium\"> of Feb, will consider their birthdate as either March 1 or Feb 28. We also assume that there are no twins in the group as they will have the same birthday. These assumptions make sure that every day in a year is equally likely to be the birthdate of the people in the group.<\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: medium\"><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\">Let there be \u2018n\u2019 people in a group. So every person in the group can have any birthday out of the 365 days. That is there are 365 possibilities for every person. Therefore the total number of permutations (or the possibilities) is 365 multiplied by itself \u2018n\u2019 times, i.e 365\u207f. Thus each one of the outcomes in the total permutations is equally probable. If n&gt;365, a birthday is bound to get repeated. Hence n&lt;=365. Arriving at the probability that at least two people will have the same birthday is tedious and hence we calculate the probability that all have different birthdays and subtract it from the total probability that is 1. (The range of probability is between 0 and 1). It can be calculated in the following way:<\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: medium\"><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\">Let\u2019s take any person from the group. That person can have his\/her birthday out of any of the 365 days. Let\u2019s take a second person from the group. This person will have a birthday on any day, except the day on which the first person has his\/her birthday. Therefore there 364 possibilities for this person. In this way, the number of possibilities reduces by 1 for every new person till the all the \u2018n\u2019 people have been considered. Hence the total number of permutations=<\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: medium\"><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\">365\u00d7(365-1)\u00d7(365-2)\u2026..\u00d7(365-n)<span style=\"color: #000000;font-family: Times New Roman;font-size: medium\">.<\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: medium\"><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\">To calculate the probability that no two people will have the same birthday, we divide the above figure by 365\u207f and subtract the value now calculated from 1.<\/span><\/span><\/span><\/p>\n<p><span style=\"font-size: medium\"><span style=\"color: #000000\"><span style=\"font-family: Times New Roman\">These are the probabilities that we get for different values of n:<\/span><\/span><\/span><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">Value of n<\/span><\/span><\/td>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">Probability<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">5<\/span><\/span><\/td>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">0.027<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">20<\/span><\/span><\/td>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">0.411<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">60<\/span><\/span><\/td>\n<td valign=\"top\" width=\"312\"><span style=\"font-size: medium\"><span style=\"font-family: Times New Roman\">0.994<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"http:\/\/www.vskills.in\/certification\/certifications\">Click here for government certifications <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>One of the most common birthdays cited in probability theory is the birthday problem where the probability that at least two people in a group of people would have their birthdays on the same day. This means that the month and day of birth is the same, but the year does not have to be&#8230;<\/p>\n","protected":false},"author":612,"featured_media":25995,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_joinchat":[],"footnotes":""},"categories":[1560],"tags":[933,2359,2358],"class_list":["post-25944","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arbit","tag-birthday","tag-permutations","tag-probability"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Birthday Problem in Probability Theory - Vskills Blog<\/title>\n<meta name=\"description\" content=\"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Birthday Problem in Probability Theory - Vskills Blog\" \/>\n<meta property=\"og:description\" content=\"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/\" \/>\n<meta property=\"og:site_name\" content=\"Vskills Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/vskills.in\" \/>\n<meta property=\"article:published_time\" content=\"2015-02-27T10:29:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-03T07:45:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"259\" \/>\n\t<meta property=\"og:image:height\" content=\"194\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Ashwini Dabadge\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ashwini Dabadge\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/\",\"url\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/\",\"name\":\"The Birthday Problem in Probability Theory - Vskills Blog\",\"isPartOf\":{\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\",\"datePublished\":\"2015-02-27T10:29:14+00:00\",\"dateModified\":\"2024-04-03T07:45:47+00:00\",\"author\":{\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/e820dd4630188d78a7436d396c52f126\"},\"description\":\"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.\",\"breadcrumb\":{\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage\",\"url\":\"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\",\"contentUrl\":\"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg\",\"width\":259,\"height\":194},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.vskills.in\/certification\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"The Birthday Problem in Probability Theory\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/#website\",\"url\":\"https:\/\/www.vskills.in\/certification\/blog\/\",\"name\":\"Vskills Blog\",\"description\":\"Vskills - A Initiative in Assessment to Enhance Employability\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.vskills.in\/certification\/blog\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/e820dd4630188d78a7436d396c52f126\",\"name\":\"Ashwini Dabadge\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8b36f2889aaacffc59878d936f8e8b924bcda62b76ad7995cf30edb8ac0912c5?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8b36f2889aaacffc59878d936f8e8b924bcda62b76ad7995cf30edb8ac0912c5?s=96&d=mm&r=g\",\"caption\":\"Ashwini Dabadge\"},\"description\":\"I am currently pursuing my Masters in Economics at University College London and a former German language translator. When not studying topics related to Economics, I can be found writing about films and the Mahabharata.\",\"url\":\"https:\/\/www.vskills.in\/certification\/blog\/author\/ashwini-dabadge\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"The Birthday Problem in Probability Theory - Vskills Blog","description":"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/","og_locale":"en_US","og_type":"article","og_title":"The Birthday Problem in Probability Theory - Vskills Blog","og_description":"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.","og_url":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/","og_site_name":"Vskills Blog","article_publisher":"https:\/\/www.facebook.com\/vskills.in","article_published_time":"2015-02-27T10:29:14+00:00","article_modified_time":"2024-04-03T07:45:47+00:00","og_image":[{"width":259,"height":194,"url":"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg","type":"image\/jpeg"}],"author":"Ashwini Dabadge","twitter_misc":{"Written by":"Ashwini Dabadge","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/","url":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/","name":"The Birthday Problem in Probability Theory - Vskills Blog","isPartOf":{"@id":"https:\/\/www.vskills.in\/certification\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage"},"image":{"@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage"},"thumbnailUrl":"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg","datePublished":"2015-02-27T10:29:14+00:00","dateModified":"2024-04-03T07:45:47+00:00","author":{"@id":"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/e820dd4630188d78a7436d396c52f126"},"description":"Learn and know one of the most common birthdays cited in probability theory is the birthday problem. Take Vskills Certification in the same. Read here.","breadcrumb":{"@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#primaryimage","url":"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg","contentUrl":"https:\/\/www.vskills.in\/certification\/blog\/wp-content\/uploads\/2015\/02\/The-Birthday-Problem-in-Probability-Theory.jpg","width":259,"height":194},{"@type":"BreadcrumbList","@id":"https:\/\/www.vskills.in\/certification\/blog\/the-birthday-problem-in-probability-theory\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.vskills.in\/certification\/blog\/"},{"@type":"ListItem","position":2,"name":"The Birthday Problem in Probability Theory"}]},{"@type":"WebSite","@id":"https:\/\/www.vskills.in\/certification\/blog\/#website","url":"https:\/\/www.vskills.in\/certification\/blog\/","name":"Vskills Blog","description":"Vskills - A Initiative in Assessment to Enhance Employability","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.vskills.in\/certification\/blog\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/e820dd4630188d78a7436d396c52f126","name":"Ashwini Dabadge","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.vskills.in\/certification\/blog\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8b36f2889aaacffc59878d936f8e8b924bcda62b76ad7995cf30edb8ac0912c5?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8b36f2889aaacffc59878d936f8e8b924bcda62b76ad7995cf30edb8ac0912c5?s=96&d=mm&r=g","caption":"Ashwini Dabadge"},"description":"I am currently pursuing my Masters in Economics at University College London and a former German language translator. When not studying topics related to Economics, I can be found writing about films and the Mahabharata.","url":"https:\/\/www.vskills.in\/certification\/blog\/author\/ashwini-dabadge\/"}]}},"_links":{"self":[{"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/posts\/25944","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/users\/612"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/comments?post=25944"}],"version-history":[{"count":6,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/posts\/25944\/revisions"}],"predecessor-version":[{"id":71513,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/posts\/25944\/revisions\/71513"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/media\/25995"}],"wp:attachment":[{"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/media?parent=25944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/categories?post=25944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vskills.in\/certification\/blog\/wp-json\/wp\/v2\/tags?post=25944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}