Tech is playing State in the last conference game of theseason. Tech is trailing State 21 to 14 with 7 seconds left inthe game, when they score a touchdown. Still trailing 21 to20, Tech can either go for two points and win or go for onepoint to send the game into overtime. The conferencechampionship will be determined by the outcome of thisgame. If Tech wins they will go to the Sugar Bowl, with apayoff of $9.2 million; if they lose they will go to the GatorBowl, with a payoff of $1.5 million. If Tech goes for twopoints there is a .30% chance they will be successful andwin (and a .70% chance they will fail and lose). If they gofor one point there is a 0.98 probability of success and a tieand a 0.02 probability of failure. If they tie they will playovertime, in which Tech believes they have only a 20%chance of winning because of fatigue.a. Use decision-tree analysis to determine if Tech shouldgo for one point or two points.b. What would Tech’s probability of winning the game inovertime have to be to make Tech indifferent betweengoing for one point or two points?
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 onepoint 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?
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