You are a contestant on the Jacob game show. Three closed doors are shown before you. Behind one of these doors is a Bike; behind the other two are Goats. The contestant does not know where is the bike, but Jacob does.

The contestant picks a door and Jacob opens one of the remaining doors, one he knows doesn’t hide the bike. If the contestant has already chosen the correct door, Jacob is equally likely to open either of the two remaining doors.

After Jacob has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the bike if he stays with his first choice? What if he decides to switch?