1. A mouse is put into a T-maze (a maze shaped like a T). In this maze, it has the choice of turning to the left and being rewarded with cheese or going to the right and receiving a mild shock. Before any conditioning takes place (i.e., on trial 1), the mouse is equally likely to go to the left or to the right. After the first trial, its decision is influenced by what happened on the previous trial. If it receives cheese on any trial, the probabilities of going to the left or right become .9 and .1, respectively, on the following trial. If it receives the electric shock on any trial, the probabilities of going to the left or right on the next trial become .7 and .3, respectively. What is the probability that the mouse will turn left on the second trial?
2. Refer to Exercise 17. What is the probability that the mouse will turn left on the third trial?
3. Three ordinary quarters and a fake quarter with two heads are placed in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH," what is the probability that the fake quarter was selected?