To select the last member of a tennis team, Alan, Bill, and Colin playoff as follows.

Two of them will be randomly chosen to play each other, and the winner will play the third person. The winner of the second game will be chosen for the team. If the probability of Alan beating Bill is 0.3, of Alan beating Colin is 0.6, and of Bill beating Colin is 0.4, draw a tree diagram to find the probability that Alan will win his way into the team.