A Rat Finishing off The Maze!
The challenge ahead of rat?
For rat, there are 2 paths viz A (5 minutes) and C (3 minutes) leading to the end while paths B (8 minutes) and D (2 minutes) lead to the start again.
Since, there are 4 paths & each having equal chance of being chosen by rat, there is 1/4 th chance for each path for to be chosen by rat.
Let's assume T be the time needed for rat to finish the maze.
But if rat selects path B or D then rat need T more time again as these paths lead to the start of the maze again.
Hence,
T = (1/4) x A + (1/4) x B + (1/4) x C + (1/4) x D
T = (1/4) x 5 + (1/4) x (8 + T) + (1/4) x 3 + (1/4) x (2 + T)
T = (5/4) + (2) + (T/4) + (3/4) + (1/2) + (T/4)
T = (9/2) + (T/2)
T/2 = 9/2
T = 9
That is rat needs 9 minutes to finish the maze.
