You receive a strange letter stating the following:
You are one of 20 logicians worldwide to receive this letter. You don't know each other, but you all think alike. An address is given, and you are told that if a letter is received from one and only one of you, all 20 will equally split a large sum of money. If no letters are received, or more than one, no prize.
What would you to for a chance of winning the prize? What could you do in order to maximise the probability of winning?
(In reply to
re: probabilistic approach - proof by Jim Lyon)
When i saw this problem the first thing that came to mind
was binomial distribution. In the equation
P(x = r) = nCr p^r(1-p)^n-r
setting r to 1 and n to 20 yields a function of the
form P(X = r) = f(p). Then, as you mention, you take
df(p)/dp. The truth was i did this but could not solve
for 0 other than via inspection, whereby it is clear that
1/N yields 0. (by the way, i believe you meant a '^'
instead of a '*' in the second term of your derivative?)
re(2): probabilistic approach - proof
