Same Day Birthday-A Paradox?

A birthday is a date on which a person breathesto play. The birthday paradox states that given a
his first outside his mother's womb and preparesgroup of 23 randomly chosen people, the
himself for a new life. It is the beginning, a windowprobability is more than 50% that at least two of
to the chance of a lifetime. It is an occasion to bethem will have the same birthday. If the number
commemorated just as a nation commemoratesof people increases to 60 or more, the probability
its birth or as an organization celebrates itsis greater than 99%. However it cannot actually
founding. However the underlying question stillbe 100% unless there are at least 366 people.
remains as to why one celebrates his birthday. IsOne should not take it to be a paradox in the
it the fact that they have survived another yeartrue sense of the word , as in the sense of
against many odds that life gave them theleading to a logical contradiction. In fact it is
opportunity to chance upon or is this day thedescribed as a paradox because mathematical
expression of a hope to live another year? Nonetruth contradicts candid or gullible intuition.
of the above, it would seem. If it is the past yearOne can try it himself. If one is at a gathering of
that one is commemorating, would he still raise a20 or 30 people, and each individual's date of birth
toast to it if he were to receive some bad news?is asked, it is likely that two people in the group
Not likely. But why? What is the relevance ofwill have the same date of birth. It always
information about the future when one issurprises people! The reason this is so surprising is
celebrating the past? This is perhaps because ofbecause an individual is used to comparing his
an astrological lore. The wise men noticed thatparticular birthdays with others. For example, if a
when the sun hit the same spot in the heavensperson meets someone randomly and asks him
that it held on a person's date of birth, that dayhis date of birth, the chance of the two of them
turned out to be extremely fortunate. This luckyhaving the same birthday is only 1/365 (0.27%)
pattern brought joy, and thus the birthday personwhich is extremely low. Even if he asks 20
wanted to celebrate.people, the probability is still low -- less than 5%.
This substantiates the fact that it is not the pastSo one feels that it is very rare to meet anyone
that is foremost on one's minds but the thewith the same date of birth as his.
future. One celebrates the success at havingWhen 20 people are put in a room, however, the
arrived so far because such successful resiliencething that changes is the fact that each of the 20
allows him to continue forward. This day is thepeople is now asking each of the other 19 people
expressions of unrestrained, unbridled, blind faith inabout their date of birth. Each individual person
one's own suspended mortality. But as oneonly has a small, less than 5%, chance of success,
moves up the ladder of age, he gets closer tobut each person is trying it 19 times. So that
the inevitable death. So we can conclude thatincreases the probability dramatically. If one wants
birthdays are about self-delusions defying death.to calculate the exact probability, one way to look
They are about preserving the sweet memoriesat it is like this. He should mark his birthday on the
of immortality. They are forms of acting outcalendar. The next person who walks in has only
one's magical thinking. By celebrating our existencea 364 possible open days available, so the
on this day, we bestow on ourselves protectiveprobability of the two dates not colliding is 364
charms against the meaninglessness and365. The next person has only 363 open days, so
arbitrariness of a cold, impersonal, and oftenthe probability of not colliding is 363/365. If one
hostile universe. It is customary in many culturesmultiplies the probabilities for all 20 people not
to celebrate this day, for example by having acolliding, then one gets: 364/365 * 363/365 * ...
party with family and/or friends.365-20+1/365 = Chances of no collisions. That is
The excitement of this occasion doubles whenthe probability of no collisions, so the probability of
one shares his birthday with another person. Incollisions is 1 minus that number. The next time
this regard the Birthday paradox has a major roleyou are with a group of 30 people, try it!