Isaac and Mary enter a quiz show and reach the final stage in which they will win the grand prize if they answer a true–false question correctly. Assume that each of them has a probability p of giving the correct answer. Before the question is posed, Isaac tells Mary that they should choose one person between them and let that person give the answer to the question. Mary, on the contrary, thinks that they should both think about the question and, if their answers agree, they should give that common answer; otherwise, they should flip a coin to see who answers the question. Which of the two strategies do you think maximizes their probability of winning the prize?