Suppose your first game is against a top team. Your probability of winning (W) is 20% (probability of losing (L)80%). If you win that game, then you play a team you have beat before and your chance of winning that game and getting into the final (F) is 60% (not winning and not getting to the final (F) is 40%).

If you lose the first game you will play a team that is a bit better than your team and the chance of winning and getting to the final (F) is 40% (not winning and not getting to the final(F)is 60%). To the right is a tree diagram showing the outcomes.

Answer the following and provide the equations you use.

a) What is the probability that your team gets to the final?

b) What is the probability that you won your first game given you made it to the final?