What are the chances of two people having the same initials?

This means that the probability of 2 individuals having the same initial first and last name will be 84.4\%.

How many people must be in a group to ensure that at least 2 individuals have the same first initial?

The +1 ensures there exist at least two people with the same initial. Maybe it would help to think of a smaller case. If one rolls a dice 6 times, it’s possible to roll a different number each time. However, rolling a dice 6+1=7 times ensures that at least one number was rolled more than once.

Is it true that within a group of 700 people there must be 2 who have the same first and last initials?

Yes. There are 262 = 676 different sets of first and last initials (pigeonholes) There are 700 people (pigeons). Absolutely. Let A and B be finite sets such that |A| > |B|.

How many students must you have in your school to guarantee that at least 2 of them have the same birthday?

By the pidgeon hole principle, you must have 102 students in class to assure that two of them get the same score.

What is the probability of two friends having their birthday on the same day in a leap year?

The first person can be born on any day of the year, this means that the probability is 365/365 = 1. The second person has to be born on the same day as the first and there is a 1/365 chance of that happening.

How common is it to have the same name and birthday?

This means that if there are only 89 records then you have ~90\% certainty that any match is the result of it being the same individual, at 468 records your certainty is down to 5\%….

Match Probability	Day and Month match	Full Date match
80\%	35 people	343 people
95\%	47 people	468 people
99\%	57 people	579 people

What are the odds that someone has the same birthday and name?

Ignoring leap years, there are 365 days in a year so the probability a given person has the same birthday as you is 1/365. Of the 620 people with the same name, we expect that 620/365 or approximately 1.7 people will have the same name and the same birthday as you.

How many students must be in a class to guarantee that atleast 2 students receive the same score on the final exam if the exam is graded on a scale from 0 to 100 points?

What is the probability that two or more people in a party with 20 people will have the same birthday?

0.411
1−0.493 = 0.507 or 50.7\%. In a randomly selected group of 23 people, it is slightly more likely than not that two or more of them share a birthday….Probability of Shared Birthdays. or, How to Win Money in Bar Bets.

Probability in a group of n people that 2 or more have the same birthday
20	0.411
22	0.476
23	0.507