Waldo is having a party and has 50 guests, among whom is his brother Basil.

Basil starts a rumor about Waldo; a person hearing this rumor for the first time will then tell another person chosen uniformly at random the rumor, with the exceptions that no one will tell the rumor to Waldo or to the person they heard it from.

If a person who already knows the rumor hears it again, they will not tell it again.

What's the probability that everyone, except Waldo, will hear the rumor before it stops propagating?

What if each person told two people chosen uniformly at random?

(In reply to re: More refined simulation for part 2 by Charlie)

Another re-run with more scrambled bits yielded 353 out of a million trials.  Adding on to the previous, that makes 1074/3,000,000 = .000358 or 1/2793.

Posted by Charlie on 2004-12-04 03:58:37