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 Probability and Statistics Basic Probability and Statistics Math Forum

 December 15th, 2007, 08:56 PM #1 Newbie   Joined: Dec 2007 Posts: 1 Thanks: 0 Birthday problem [statistics] Well, I was just googling some math puzzles (how nerdy,) but anyways... I came across this one: http://mathforum.org/dr.math/faq/faq.birthdayprob.html Now, the question poses something along the lines of "how many students would need to be in a class in order for the probability of at least 2 to have the same birthdays be >= 50%." Now, I view this as a binomial distribution. let X = the event that 2 or more students have the same birthday. P(X >= 2) = ∑[(n over k)(p^k*(1-p)^(n-k))] where k = {2,3,4,...n) and n = class size. Formula can be found here: http://en.wikipedia.org/wiki/Binomial_distribution. First find the probability 2 or more students have the same birthday of a single day, say January 1st. Suppose p = the probability of a student having a birthday on a single day of the year: 1/365 ~ .0027 n = class size = unknown variable k = {2,3,4...n) In order to consider all days of the year, we multiply the P(X >= 2 | day is January 1st) * 365. Now if we just brute force this, plugging in 23 for class size (as suggested) gives you a probability of .6671, much higher than 50%. The get the closest value, 20 should be defined as n, giving you a probability of .5037. Is there anything wrong with my thinking or calculations? December 16th, 2007, 03:11 AM   #2
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 Originally Posted by XTTX Is there anything wrong with my thinking or calculations?
Yes, since "23" is correct. Your figure for the associated probability is incorrect. December 18th, 2007, 12:50 PM #3 Senior Member   Joined: Oct 2007 From: France Posts: 121 Thanks: 1 let A= the event that 2 or more students have the same birthday Let B be the complementary event (all the birthdays are different). We want P(B)<=0,5. We have P(B)=A(365,n)/365^n, where A(365,n) is the number of arrangements of 365 days taken n at a time, namely: A(365,n)=365*364*..*(365-n+1) It is easy to verify that P(B)<=0,5 for n>=23. Tags birthday, problem, statistics Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nishant746 Advanced Statistics 7 April 2nd, 2012 06:20 AM azizlwl Advanced Statistics 1 March 4th, 2012 03:10 PM NeuroFuzzy Advanced Statistics 3 December 1st, 2010 10:12 PM Randomas Advanced Statistics 10 May 30th, 2010 02:24 AM aleph_01 Advanced Statistics 2 September 30th, 2009 12:00 PM

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