On a certain island each of the inhabitants is a member of one of the two existing clubs.

The membership distribution is such that when two random people meet, the probability of those two belonging to the same club is equal to the probability of them belonging to distinct clubs.

When 100 newcomers arrive on the island and each enrolls in one of the two clubs, the distribution still retains this feature. How many people belong to either club?

(In reply to First meeting by Leming)

Well, Dan, to help along those lines... say there are 4 people on the island (A, B, C, and D).

Assume A belongs to club X, and B, C, and D all belong to club Y.

The possible pairings (equally likely random meetings) are:
AB
AC
AD
BC
BD
CD

In the first three cases (50%) the pairing is in different clubs.
In the second three cases (50%) the pairing is in the same club.

... continue from here ... :-)

Posted by Thalamus on 2004-06-17 13:54:02