There's a mouse and three doors:
The first door takes the mouse to a cheese in 3 minutes.
The second door takes the mouse to the initial state (he has to choose a door again) in 5 minutes.
The third door takes the mouse to the initial state in 5 minutes.
Always the mouse chooses a door randomly and independient.
What's the expected value of the time the mouse takes to get the cheese?
i would really apreacciate a help here