2. Each year, the Huskies play 12 football games. Some years, they are Good in which case they win , of their games; some years, they are Average in which case they win ? of their games; and some years, they are Bad in which case they win , of their games. Consider Freddy, whom we discussed in class. Freddy believes there is an urn containing 12 balls, each ball is labeled either "Win" or "Lose." When the Huskies are Good, 8 of the balls say "Win," and only 4 say "Lose." When the Huskies are Average, 6 of the balls say "Win" and 6 say "Lose." When the Huskies are Bad, 4 of the balls say "Win," and 8 of the balls say "Lose." Every time the Huskies play a game, Freddy believes that one of these balls is randomly drawn from the urn without replacement. (a) Suppose that the Huskies are in fact Good, and Freddy realizes this. If the results of the first five games have been LLWWL, what does Freddy believe is the prob- ability that the Huskies will win their next game? What is the actual probability that they will win the next game? (b) If they lose their sixth game, what will Freddy believe the likelihood of winning the seventh game will be? If they lose their sixth game, what will Freddy believe the likelihood of winning their seventh game will be? Name the bias that afflicts Freddy's decision-making. (c) The results of the first nine Huskies games were LLWWLLWWL. Does Freddy still believe that the Huskies are good? Name the bias that afflicts Freddy's decision-making (d) If the Huskies are Good, what is the probability that they produce this exact result? What if the Huskies are Average? What if the Huskies are Bad? (e) At the start of the season, suppose that it is equally likely that the Huskies are Good, Average, or Bad (That is, Pr(Good)=Pr(Average)=Pr(Bad)=1). Given that you observed the results from the first nine games, what is the likelihood that the Huskies are Good? [Calculate Pr(Good results of first nine games).] (f) Compare the result in (e) to the result in (c). Argue that Freddy is too quick to jump to conclusions