In a bicycle race between two competitors, let Y(t) denote the amount of time (in seconds) by which the racer that started in the inside position is ahead when 100t percent of the race has been completed, and suppose that

{Y(t), 0  t  1} can be effectively modeled as a Brownian motion process with variance parameter σ2.

(a) If the inside racer is leading by σ seconds at the midpoint of the race, what is the probability that she is the winner?

(b) If the inside racer wins the race by a margin of σ seconds, what is the probability that she was ahead at the midpoint?