0 votes 0 votes How many people must there be in a room before there is a 50% chance that two of them were born on the same day of the year? At least 23 At least 183 At least 366 At least 730 Probability probability ugcnetcse-sep2013-paper3 + – Sanjay Sharma asked May 4, 2016 recategorized Oct 19, 2018 by Pooja Khatri Sanjay Sharma 2.2k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 3 votes 3 votes Atleast 23 People This is standard problem known as Birthday problem. Source:https://en.wikipedia.org/wiki/Birthday_problem ManojK answered May 4, 2016 selected Jan 4, 2017 by Sanjay Sharma ManojK comment Share Follow See all 3 Comments See all 3 3 Comments reply srestha commented May 4, 2016 reply Follow Share I am not getting how they calculated 23 0 votes 0 votes ManojK commented May 4, 2016 reply Follow Share @srestha check these lines the probability, P(1), that Person 1 does not share his/her birthday with previously analyzed people is 1, or 100%. Ignoring leap years for this analysis, the probability of 1 can also be written as 365365, for reasons that will become clear below. For Event 2, the only previously analyzed people are Person 1. Assuming that birthdays are equally likely to happen on each of the 365 days of the year, the probability, P(2), that Person 2 has a different birthday than Person 1 is 364365. This is because, if Person 2 was born on any of the other 364 days of the year, Persons 1 and 2 will not share the same birthday. Similarly, if Person 3 is born on any of the 363 days of the year other than the birthdays of Persons 1 and 2, Person 3 will not share their birthday. This makes the probability P(3) = 363365. This analysis continues until Person 23 is reached, whose probability of not sharing his/her birthday with people analyzed before, P(23), is 343365. P(A') is equal to the product of these individual probabilities: (1) The terms of equation (1) can be collected to arrive at: (2) Evaluating equation (2) gives P(A') ≈ 0.492703 3 votes 3 votes srestha commented May 4, 2016 reply Follow Share oh yes , got atleast :) 1 votes 1 votes Please log in or register to add a comment.