Question

A group of 100 people are comparing their birthdays (as usual, assume their birthdays are independent and not on February 29, etc.). Find the expected number of pairs of people with the same birthday, and the expected number of days in the year on which at least two of these people were born.

20 Feb 2025
Answer :
Word Count : 637

To address the problem, let's break it down into two parts as specified:

Part 1: Expected Number of Pairs of People with the Same Birthday

We are given a group of 100 people, and we want to determine the expected number of pairs of people who share the same birthday. The key assumption here is that birthdays are independent and randomly distributed across the 365 days of the year.

Step 1: Probability of a Pair Sharing a Birthday

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