The birthday problem is: What is the probability of two or more people out of a of do have the same birthday?
Solution. Let be the event two or more people out of a group of to have the same birthday. It is easy to find first the complement of , , which is that no two people out of a group of will have matching birthdays out of (number of days of one year) equally possible birthdays. We start with an arbitrary person’s birthday. So the second person’s birthday in order to be different from the first one gives us the probability, . Consecutively, the third person’s birthday is different from the first two and we have . Finally for the the th person’s birthday we get the probability
By the last expression of the estimated probability we can see that there exists another easier approach to find the probability which is the following:
We set the possible ways for birthdays, as the denominator.
Therefore we have
The table below shows the probability for some values of
|Date of creation||2013-03-22 16:09:38|
|Last modified on||2013-03-22 16:09:38|
|Last modified by||PrimeFan (13766)|