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 black ball?

Try to guess (=estimate guided by intuition), then evaluate.
You'd be surprised.

Source: A.E. Lawrence, “Playing With Probability”
Mathematical Gazette, (1969)

(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.

Please comment.

   

Edited on September 5, 2015, 1:08 am

Posted by Ady TZIDON on 2015-09-05 00:57:44