In the second quarter of Super Bowl 47, the Baltimore Ravens tried to surprise the San Francisco 49ers with a fake field goal attempt. It didn't work then, but it might be a good strategy in certain circumstances. Suppose your team was winning 14-3 in the second quarter. Your team is in a fourth-and-goal situation on the 5-yard line. If your team kicks the field goal (assuming they have a 100% chance of making it from this short distance), you will go up 17-3 and have a win probability of 0.904. If the team fakes the field goal attempt and scores a touchdown, you will go up 21-3 and have a win probability of 0.955. However, if your team fakes the field goal and doesn't score, thereby giving the ball to the opponent, your team will have a win probability of 0.858.
Create a tree diagram for a fake field goal attempt, using the possible outcomes of the attempt as the first set of branches and the possible outcomes of the game as the second set of branches. Assume that your team has a 0.50 probability of scoring a touchdown on a fake field goal attempt. Then calculate probabilities of all of the outcomes. Round to the thousandths when necessary.