I am a contestant on the popular TV show “Tired of Fortune.” During the bonus round, I will be asked up to four questions. For each question that is correctly answered, I win a certain amount of...

I am a contestant on the popular TV show “Tired of Fortune.” During the bonus round, I will be asked up to four questions. For each question that is correctly answered, I win a certain amount of money. One incorrect answer, however, means that I lose all the money I have previously won, and the game is over. If I elect to pass, or not answer a question, the game is over, but I may keep what I have already won. The amount of money I win for each correct question and the probability that I will answer each question correctly are shown in Table.

a My goal is to maximize the expected amount of money won. Use dynamic programming to accomplish this goal.

b Suppose that I am allowed to pass, or not answer a question, and still go on to the next question. Now determine how to maximize the amount of money won.