mpresic
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- 128
I did not mix the problems up but please take away the "birthday" It is just the Cereal problem.
mfb said:Well if the formula assumes something that is not true, the formula does not work.
OK first of all I apologize for not having my LATEX skills in order...anyway for #5...each generation r exposes 2^r inhabitants to the rumor out of a pool of (n+1) inhabitants. That means that ((n+1)-2^r) inhabitants are not exposed to the rumor during the rth generation and the odds of being in this pool of unexposed inhabitants is:In a town of n+1 inhabitants. A person tells a rumor to two distinct numbers, the "first generation". These repeat the performance and generally, each person tells a rumor to two people at random without regard to the past development. Find the probability that the generation r will not contain the person who started the rumor. Find the median of this distribution assuming n large.
My apologies. Someone posted my exact thought process and was corrected in the same manner...mfb said:@rjbeery: that value gets negative for large r.
People can tell the rumor to people who know it already, so the 2r assumption does not work. This has been discussed in the thread already.
It is zero, Alice and Bob can't directly tell the rumor back to the person they got it from.Megaquark said:Since he has to choose 2 distinct people, let's say he told Alice and Bob, the probability he'll be told by Alice is p=(1/n)+[1/(n-1)]. The probability he'll be told by Bob is the same.
mfb said:It is zero, Alice and Bob can't directly tell the rumor back to the person they got it from.
Alice can tell it to Bob, however, and Bob also to Alice, which generates another two cases (different in the next generation due to more correlated forbidden rumor directions).
A tells B and C, B tells A and C
A tells B and C, B tells A and D
TheBlackAdder said:Btw, these challenges should happen regularly. They're awesome!