If you take a group of people born in a non leap year you would need 366 people for a 100% chance that someone shares a birthday but only 23 people for a 50% chance that somebody shares a birthday?
In: Mathematics
A person can be born in any 365 days. Now if you have another person, they have only 364 possible birthdays so they don’t match any. Third person has only 363 valid birthdays.
By doing this, you could in theory list all the possible alternatives.
Person 1 on Jan 1st, Person 2 on Jan 2nd , Person 3 on Jan 3rd. Hey they are different days!
Okay, how about Person 1 on Jan 1st, Person 2 on Jan 2nd , Person 3 on Jan 1st. Oh, now those two share a birthday.
List down all possible answers. If you have 23 people, and you list all the possible combinations, there are more of the combinations where two people are on the same day, than those combinations where they dont.
Luckily you dont have to list them all you can calculate it. Take the valid combinations and divide by the total.
(365*364*363*…*343) / (365²³)
Latest Answers