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?
Most people answer 4, but in fact the first black ball is most likely to appear on the very first draw:
By symmetry, the second black ball is most likely to appear on the final draw.
(A.E. Lawrence, “Playing With Probability,” Mathematical Gazette, vol. 53 [December 1969], 347-354.)