In American football, touchdowns are worth 6 points. After scoring a touchdown, h scoring team may subsequently attempt to score 1 or 2 additional points. Going for 1 point is virtually an assured success, while going for 2 point is successful only with probability p. Consider the following game situation. The Temple Wildcats are losing by 14 points to the Killeen Tigers near the end of regulation time. The only way for Temple to win (or tie) this game is to score two touchdowns while not allowing Killeen to score again. The Temple coach must decide whether to attempt a 1-point or 2-point conversion after each touchdown. If the score is tied at the end of regulation time, the gam goes into overtime. The Temple coach believes that there is a 50% chance that Temple will win if the game goes into overtime. The probability of successfully converting a 1-point conversion is 1.0 The probability of successfully converting a 2-point conversion is p.
Assume Temple will score two touchdowns and Killeen will not score. Create a decision re for the decision of whether Temple’s coach should go for a 1-poin conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should b either WIN or LOSE for Temple
Assume that a WIN results in a value of 1.0 and LOSE results in a value of 0. Further, assume that the probability of converting a 2-point conversion is p= 0.4. Should Temple’s coach go for a 1-point conversion o 2-point conversion after scoring the first touchdown?