A woman is trapped in a room at the center of a maze. The room has three exits. Exit 1 leads outside the maze after 3 minutes, on average. Exit 2 will bring her back to the same room after 5 minutes. Exit 3 will bring her back to the same room after T" minutes. Assume that every.r time she makes a choice, she is eoualII...r lilreII...r to choose any exit. What is the expected time taken bv her to leave the maze?I Hint: Let X = time taken by the woman to leave the maze from this room. Let 'I" = exit she chooses first. So '1" belongs in {1, 2, 3}. Calculate the conditional expectation of time taken to leave the maze given that she chose each of the exits. Then use these conditional expectations to calculate the expectation of time taken to leave the maze. nun: fun I .1 our. "r-MI I I_ .- 41' M3