One of the most famous probability problems (sometimes called the "Birthday Paradox") is calculating how many randomlychosen people you would need for a 50% chance that at least two have the same birthday. Let's calculate the probability that none of the randomlychosen people can have the same birthday. The probability of the first person having any birthday is (365 ÷ 365) which equals 1.
We know that the second person cannot have the same birthday as the first person so we calculate
The probability of the third person having any birthday except for person 1 or person 2's birthday is:
The probability of the fourth person having any birthday except for person 1, person 2 or person 3's birthday is:
We can carry out these calculations until the probability falls below .5 because we are looking for the probability that none of the chosen people have the same birthday.
As we can see, when we choose 23 people, the probability falls below .5 and
here is the actual calculation of that probability: Then, all we have to do is subtract this number from 1 to get the probability that both have the same birthday.
To see how accurate this is, let's take a real world example.
When it comes to dates of death, the coincidences are more plentiful.
To calculate the probability of three or more people having the same birthday, click here.

