A group of freshmen at a local university consider joining the equestrian team. Students choose Western riding with probability P = .35, dressage with probability P=0.45, and jumping with probability P = 0.40. The probability that a student chooses both dressage and jumping is P = 0.15, while the probability of a student choosing Western and dressage is P = 0.10. No one chooses Western and jumping. There are no horses suitable for both and each student is assigned to one horse. If two students decide to join the team, what is the probability that both are Western and dressage riders if they independently decide?
