I see,b to recall from an old textbook that the probability to have at least one 
person having his/her  birthday at a party attended by 20 people is about 50%.

It was a fairly simple formula to derive that result but it has beeen 20 years...

Hello Francois777,

The following question is more common and known as the "Birthday
Problem", and likely what you remember from the textbook. It's
actually about the probability of two people sharing the same birthday
on a party. Following page explains the calculation:

The Birthday Problem
http://members.tripod.com/%7EProbability/birthday.htm
"If birthdays can be considered to occur at random, 23 guests are
sufficient to ensure a 50% probability that at least two will have the
same birthday."

To many people, the number 23 is suprisingly low, and some would guess
183.
The problem is also explained at the following page:

Same.day
http://rec-puzzles.org/new/sol.pl/probability/birthday/same.day

And in this very complete article:

Ivars Peterson's MathTrek - Birthday Surprises
http://www.maa.org/mathland/mathtrek_11_23_98.html

Related to that:

Devlin's Angle
http://www.maa.org/devlin/devlin_4_00.html

You can find a list of all probabilities at:

Birthday Probabilities
http://tag.publication.org.uk/birthdays.php


Hope it helps!


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