the smallest number of people in a room where the probability of two of them having the same birthday is at least 50 percent. Answer is between 1 and 31.


This is a classic problem given in probability classes. There are plenty of sites which will give and explain the answer, including Wikipedia.
google, "birthday", "probability", "room"

thanks!!

0.212 divided into 1.696= what

You're welcome! To find the smallest number of people in a room where the probability of two of them having the same birthday is at least 50 percent, you can follow these steps:

1. Begin by considering the opposite scenario: the probability of all individuals in the room having different birthdays.
2. Take the first person in the room and consider their birthday as fixed. The probability of the second person not sharing the same birthday is 364/365 (since there are 365 days in a year).
3. For the third person, the probability of them not sharing a birthday with either the first or second person is (364/365) * (363/365).
4. Continue this process, multiplying the probabilities of each subsequent person not sharing a birthday with any of the previous ones.
5. Keep adding people to the room and calculating the probability until the cumulative probability of them all having different birthdays is less than 50 percent.
6. The number of people in the room at this point is the smallest number where the probability of two people having the same birthday is at least 50 percent.

If you prefer a quicker way of finding the answer, you can search "birthday probability problem" or "birthday paradox" on a search engine like Google. There are many resources available, including Wikipedia, that explain this problem in detail and provide the answer for you.