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 Tech scores a touchdown. Still trailing 21 to 20, Tech can either go for 2 points and win or go for 1 point to send the game into overtime. The conference championship will be determined by the outcome of this game. If Tech wins, it will go to the Sugar Bowl, with a payoff of $7.2 million; if it loses, it will go to the Gator Bowl, with a payoff of $1.7 million. If Tech goes for 2 points, there is a 33% chance it will be successful and win (and a 67% chance it will fail and lose). If it goes for 1 point, there is a 0.98 probability of success and a tie and a 0.02 probability of failure. If the teams tie, they will play overtime, during which Tech believes it has only a 20% chance of winning because of fatigue. a. Use decision tree analysis to determine whether Tech should go for 1 or 2 points. b. What would Tech’s probability of winning the game in overtime have to be to make Tech indifferent to going for either 1 or 2 points?
Unitary Method
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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 Tech scores a touchdown. Still trailing 21 to 20, Tech can
either go for 2 points and win or go for 1 point to send the game into overtime. The conference
championship will be determined by the outcome of this game. If Tech wins, it will go to the
Sugar Bowl, with a payoff of $7.2 million; if it loses, it will go to the Gator Bowl, with a payoff
of $1.7 million. If Tech goes for 2 points, there is a 33% chance it will be successful and win
(and a 67% chance it will fail and lose). If it goes for 1 point, there is a 0.98
and a tie and a 0.02 probability of failure. If the teams tie, they will play overtime, during
which Tech believes it has only a 20% chance of winning because of fatigue.
a. Use decision tree analysis to determine whether Tech should go for 1 or 2 points.
b. What would Tech’s probability of winning the game in overtime have to be to make Tech indifferent
to going for either 1 or 2 points?
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