How many people do you need to gather to be sure that at least two of them have birthdays in the same month?

In a room of just 23 people there’s a 50-50 chance of at least two people having the same birthday. In a room of 75 there’s a 99.9\% chance of at least two people matching.

What is the probability that in a classroom of 20 each person has a distinct birthday?

We want both of these events to happen so multiply the probabilities: The probability that any randomly chosen 2 people share the same birthdate. So you have a 0.27\% chance of walking up to a stranger and discovering that their birthday is the same day as yours. That’s pretty slim.

How many people should be invited to a party in order to make it likely that there are two people with the same birthday?

How many people must be there in a room to make the probability 100\% that at-least two people in the room have same birthday? Answer: 367 (since there are 366 possible birthdays, including February 29).

How do you find the probability that two people have different birthdays?

Multiply those two and you have about 0.9973 as the probability that any two people have different birthdays, or 1−0.9973 = 0.0027 as the probability that they have the same birthday. (b) Now add a third person.

How many birthdays are there in the world?

There are 365 possible birthdays. (To keep the numbers simpler, we’ll ignore leap years.) The key to assigning the probability is to think in terms of complements: “Two (or more) people share a birthday” is the complement of “All people in the group have different birthdays.”

How many people share a birthday with each other?

If there are 366 or more people, but only 365 possible birthdays disregarding leap year, then two or more of them mustshare a birthday. Here are some sample results:

What is the problem scenario for birthdays?

The same principle applies for birthdays. Instead of finding all the ways we match, find the chance that everyone is different, the “problem scenario”. We then take the opposite probability and get the chance of a match. It may be 1 match, or 2, or 20, but somebody matched, which is what we need to find.