This phenomenon actually has a name -- it is called the birthday paradox, and it turns out it is useful in several different areas (for example, cryptography and hashing algorithms).
You can try it yourself -- the next time you are at a gathering of 20
or 30 people, ask everyone for their birth date. It is likely that two
people in the group will have the same birthday. It always surprises
people! (click below to read more)
The reason this is so surprising is because we are used to
comparing our particular birthdays with others. For example, if you
meet someone randomly and ask him what his birthday is, the chance of
the two of you having the same birthday is only 1/365 (0.27%). In other
words, the probability of any two individuals having the same birthday
is extremely low. Even if you ask 20 people, the probability is still
low -- less than 5%. So we feel like it is very rare to meet anyone with
the same birthday as our own.
When you put 20 people in a room,
however, the thing that changes is the fact that each of the 20 people
is now asking each of the other 19 people about their birthdays. Each
individual person only has a small (less than 5%) chance of success, but
each person is trying it 19 times. That increases the probability
dramatically.
If you want to calculate the exact probability, one
way to look at it is like this. Let's say you have a big wall calendar
with all 365 days on it. You walk in and put a big X on your birthday.
The next person who walks in has only a 364 possible open days
available, so the probability of the two dates not colliding is 364/365.
The next person has only 363 open days, so the probability of not
colliding is 363/365. If you multiply the probabilities for all 20
people not colliding, then you get:
364/365 * 363/365 * … 365-20+1/365 = Chances of no collisions
That's the probability of no collisions, so the probability of collisions is 1 minus that number.
No comments:
Post a Comment