As the final rider in the final 60 km ti1ne trial of the Tour de France, Roy must finish in time T < 1 hour to win the Tour. He has the choice of bike made of (1) carbon fiber or (2) titanium. On the carb on fiber bike, his speed V over the course is the continuous uniform random variable with E[V] = 58 km/hr and Var[V] = 12. On the titanium bike, V is the exponential random variable with E[V] = 60 km/ hr. (a) Roy chooses his bike to maximize P[W], the probability he wins the Tour. which bike does Roy choose and what is P[W]? (b) Suppose instead that Roy flips a fair coin to choose his bike. What is P[W]