Suppose that you have two possible choices, A and B. You make the choice in a sequence of trials. A and B look the same to you at first and you are equally likely to pick each of them in the first trial. Your play is consistent with a reinforcement learning model. Suppose that your = 1/2 .

a) Suppose that you choose A in your first trial. You receive a payoff of 1. What is the likelihood that you choose A again in the second trial?

b) Suppose now, after you have chosen A in the first trial and received a payoff of 1, that you choose B in your second trial. You receive a payoff of 2. What is the likelihood that you choose B again in the third trial?