Ryan has a pet rat Romeo that he boasts is the smartest rat in the county. Sammy overheard Ryan at the county fair claiming that Romeo could learn to run a particular maze and find the cheese at the end. "I don't think Romeo is that smart!" Sammy declares. "I think the rat just chooses a random path through the maze." Ryan has built a maze with the floor plan shown at right. In addition, he has placed some cheese in an airtight container (so Romeo cannot smell the cheese) in room A. a. B A Suppose that every time Romeo reaches a split in the maze, he is equally likely to choose any of the paths in front of him. Choose a method and calculate the probability that Romeo will end up in each room. In a sentence or two, explain why you chose the method you did. b. If the rat moves through the maze randomly, out of 100 attempts, how many times would you expect Romeo to end up in room A? How many times would you expect him to end up in room B? Explain.