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# Decision Tree

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 the sugar bowl, with a payoff of 7.2 million; if it loses, it will go to the gator bow, 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 .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?

#### Solution Summary

This solution is comprised of a detailed explanation of the various aspects of Decision Tree Analysis, like Expectation Value, Probability etc. Step-by-step calculation of these complicated topics provides students with a clear perspective of Decision Tree.

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