Suppose we put eight white and two black balls into a bag and then draw forth the balls one at a time.
If we repeat this experiment many times, which draw is most likely to produce the first
Try to guess (=estimate guided by intuition), then evaluate.
You'd be surprised.
Source: A.E. Lawrence, “Playing With Probability”
(In reply to Intuition
by Steve Herman)
I liked your reasoning and would prefer it over others as "the official explanation".
However it's obvious that the statement
Let P(n) = prob that the nth draw is black"
is NOT applicable to n=0.
When you state "The smallest P2 is P2(0) = 0."you probably mean
"The smallest P2 is P2(1) = 0." i.e. no way you get the last ball on the 1st drawing.
Edited on September 5, 2015, 1:08 am