My Math Forum Probability to be born on a specific day

 Probability and Statistics Basic Probability and Statistics Math Forum

December 5th, 2016, 11:28 AM   #1
Newbie

Joined: Dec 2016
From: kljlçjkçlkjç

Posts: 1
Thanks: 0

Probability to be born on a specific day

Problem:

Quote:
 As an example, consider the scenario in which a teacher with a class of 30 students asks for everybody's birthday (for simplicity, ignore leap years), to determine whether any two students have the same birthday (corresponding to a hash collision as described further). Intuitively, this chance may seem small. If the teacher picked a specific day (say September 16), then the chance that at least one student was born on that specific day is 1 - (364/365)^{30}, about 7.9%. However, the probability that at least one student has the same birthday as any other student is around 70% for n = 30, from the formula 1-365!/((365-n)! * 365^n).
https://en.wikipedia.org/wiki/Birthday_attack

I don't understand the two formulas (for getting 7.9% and for 70%).

 December 5th, 2016, 02:12 PM #2 Global Moderator   Joined: May 2007 Posts: 6,133 Thanks: 468 Prob. not a specified date (Sep. 16) for one person is 364/365. Birthdays are assumed independent, so prob. that n people's birthday is not on specified date is $\displaystyle (\frac{364}{365})^n$, based on general rule that the probability of n independent events all happening is the product of the individual probabilities. For the second question: The probability that two people have different birthdays is 364/365. For 3 people it is (364/365)(363/365). etc. Thanks from alksdfj

 Tags born, day, probability, specific

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post William Labbett Trigonometry 2 January 4th, 2015 02:18 PM andreaugust Number Theory 2 July 15th, 2013 05:30 AM azarat Algebra 4 December 9th, 2009 06:39 PM James S Saint Advanced Statistics 12 November 4th, 2009 01:12 PM durexlw Algebra 0 April 5th, 2009 04:54 AM

 Contact - Home - Forums - Top