Tech is playing State in the last conference game of the season. Tech is trailing State 21 to 14 with 7 seconds left in the game, when they score a touchdown. Still trailing 21 to 20, Tech can either go for two points and win or go for one point to send the game into overtime. The conference championship will be determined by the outcome of this game. If Tech wins they will go to the Sugar Bowl, with a payoff of $9.2 million; if they lose they will go to the Gator Bowl, with a payoff of $1.5 million. If Tech goes for two points there is a .30% chance they will be successful and win (and a .70% chance they will fail and lose). If they go for one point there is a 0.98 probability of success and a tie and a 0.02 probability of failure. If they tie they will play overtime, in which Tech believes they have only a 20% chance of winning because of fatigue.
a. Use decision-tree analysis to determine if Tech should go for one point or two points.
b. What would Tech’s probability of winning the game in overtime have to be to make Tech indifferent between going for one point or two points?