lew@ihuxr.UUCP (09/22/83)
Words cannot express my mortification. It looks like Jim Balter's derivation is perfectly sound, after all. I didn't like Jim's justification for taking n times the probability of n-1 points falling in a fixed semicircle to get the answer. I really butchered my paraphrase of this step, I should have said: "The probability of a thing happening once in N tries is N times the probability of a thing happening once in 1 try." Of course, this ISN'T true for independent events, but as Jim stated, the events here are mutually exclusive. It is an elementary theorem that the probability of the union of a set of mutually exclusive events is the sum of their probabilities. I don't know what my problem was. Splattered all over the net ... Lew Mammel, Jr. ihuxr!lew