Final answer:
To determine the probability that at least two people share a birthday in a room, calculate the probability that all have different birthdays and subtract from 1. For 23 or more people, this probability is over 50%.
Step-by-step explanation:
The question asks about the probability that at least two people in a room have the same birthday, commonly known as the birthday problem. To find this, we first calculate the probability that all people have different birthdays and subtract it from 1.
Assuming there are n people in the room and excluding leap years, the first person can have any birthday, the second can have any of the remaining 364 days, the third 363 days, and so on. The probability that all n people have different birthdays can be calculated by multiplying these probabilities together.
If n is 23 or higher, there's more than a 50% chance that at least two people share the same birthday. This phenomenon can seem counterintuitive at first glance but is a well-known statistical concept.