Birthday Probability Problems: IITJEE Advanced Mathematics

In the following problems, each year is assumed to be consisting of 365 days (no leap year):

  1. What is the least number of people in a room such that it is more likely than not that at least two people will share the same birthday?
  2. You are in a conference. What is the least number of people in the conference (besides you) such that it is more likely than not that there is at least another person having the same birthday as yours?
  3. A theatre owner announces that the first person in the queue having the same birthday as the one who has already purchased a ticket will be given a free entry. Where (which position in the queue) should one stand to maximize the chance of earning a free entry?

I will put up the solutions on this blog tomorrow. First, you need to make a whole-hearted attempt.

Nalin Pithwa.

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