Consider an ant in a 1 by 5 grid that contains an ant and a piece of food. The piece of food is located in an unknown cell that is selected at random. The ant's position and movement are fully observable and the ant's behavior is defined as follows. 1. If the food is located to the left of the ant, the ant will move left with a .5 probability, move right with a .2 probability and remain in the same cell with a .3 probability. 2. If the food is located to the right of the ant, the ant will move right with a .5 probability, move left with a .2 probability and remain in the same cell with a .3 probability. 3. If the food is located in the same cell as the ant, the ant will move right with a .25 probability, move left with a .25 probability and remain in the same cell with a .5 probability. 4. If the ant tries to move to the right while in the rightmost cell or to the left while in the leftmost cell it will remain in the same cell. The ant starts in cell 2 and its first three moves are a move to the right, a second move to the right and a move to the left (so that it is in cell 3). a) Given these three moves, what is the probability that the food is located in each of the grid cells?
b) What is the probability that the ant will select each move (left, right, stay in cell) as its fourth move.