A Little League Baseball team has been using an automatic pitching machine. If the machine is correctly set up (i.e. properly adjusted) it will pitch strikes 85% of the time. If it is incorrectly set up, it will pitch strikes only 35% of the time. Past experience indicates that 75% of the setups of the machine are correctly done. After the machine has been set up at batting practice one day, it throws three strikes on the first three pitches. What is the revised probability that the setup has been done correctly? [Note: Every pitch is independent of the preceding pitch] What I want you to do is tell me what is the probability of winning if you switch to door C? Please explain the answer using conditional probabilities. The problem reproduced from the lecture notes is as follows, You are a contestant on a game show, and the prize of your dreams is behind either door A, B, or C. Behind the other two doors is nothing at all. You can see all three closed doors, and you have no hints. While the crowd shouts its encouragement, you think it over, make up your mind on door A, and tell everyone which door you choose. But before opening your choice of door, they tell you that they will first open a different door that does not have the prize behind it. They open door B and there is no prize behind it. After they do this, they offer you a chance to switch. There are now two doors left unopened, A and C. Should you switch to door C?