A dog is trapped in a cave. It needs to choose one of two directions. If it goes to the left, then it will walk around in the cave for five minutes and will then return to its initial position. If it goes to the right, then with probability 1/4 it will depart the cave after four minutes of traveling, and with probability 3/4 it will return to its initial position after seven minutes of traveling. Assuming that the dog is at all times equally likely to go to the left or the right, what is the expected number of minutes that it will be trapped in the cave