ABSTRACT
T he birthday problem is a classic probability problem thatgoes like this: how many randomly picked people (no twins)must be assembled before there is an even chance or higher that two or more of them will share a birthday? The answer is 23, if we assume that each day of the year is equally likely as a birth date.
If you aren’t familiar with this problem, this number might seem surprisingly low. You might be tempted to guess much higher, say, somewhere around 183. But if you really think about it, 23 is not so surprising after all: how often did two or more of your classmates in grade school have birthdays on the same day? BBC journalist James Fletcher conducted an interesting empirical study that reinforces these findings. During the 2014 World Cup soccer championship, 32 national teams of 23 players each took part. It turned out that exactly 16 of those teams had at least one double birthday, the Dutch national team (my pick!) included.1 Another real-world example concerns the birth dates of American presidents. There have been 44 presidential births, and for a randomly formed group of 44 persons there is a probability of 93.3% that at least two persons will have been born on the same day. Among the 44 American presidents, there is one such coincidence: Warren G. Harding and James K. Polk were both born on November 2.
