Question
You are on a game show with $3$ doors in front of you. One of the doors has $\$1$ million inside, while the other two are empty. In the final round, the host lets you spin a wheel two times that may reveal which door the $\$1$ million is in. On each spin, this wheel will tell you the location of the $\$1$ million $3/5$ of the time, independent between spins. Otherwise, it tells you nothing about the location of the money. After two spins, if the wheel has not revealed to you the location of the $\$1$ million, you must guess uniformly at random. What is the probability you locate the $\$1$ million door?