In American football, touchdowns are worth 6 points. After scoring a touchdown, the 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 points 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 win n (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 game goes into overtime. The Temple coach believes that there is a 46% 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. a. Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1-point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or LOSE for Temple. Success (p)
In American football, touchdowns are worth 6 points. After scoring a touchdown, the 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 points 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 win n (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 game goes into overtime. The Temple coach believes that there is a 46% 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. a. Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1-point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or LOSE for Temple. Success (p)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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B) Assume that a WIN results in a value of 0. Further, assume that the probability of converting a 2-point conversion is p=39%. Should Temple’s coach go for a 1-point conversion or 2-point conversion after scoring the first touchdown?
The Temple coach will ______(should go or should not go) for 2 points after first touchdown.
Transcribed Image Text:Go for 2
1
Success
2
Go for 2
3
Go for 1
Go for 2
4
Go for 1
Go for 2
5
Go for 1
04
7
8
9
Success (p)
Fail (1-P)
Success (p)
Fail (1-P)
Success (p)
Fail (1-P)
Win OT
(46%)
Lose OT
(54%),
10
11
Win OT
(46%)
Lose OT
(54%)
Win OT
(46%)
Lose OT
(54%)
diter each touchdown. The terminal nodes in the decis
Transcribed Image Text:eBook
Problem 4-05 (Algorithmic)
In American football, touchdowns are worth 6 points. After scoring a touchdown, the 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 points 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 game goes into overtime. The Temple coach believes that there is a 46% 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.
a. Assume Temple will score two touchdowns and Killeen will not score. Create a decision tree for the decision of whether Temple's coach should go for a 1-point conversion or a 2-point conversion after each touchdown. The terminal nodes in the decision tree should be either WIN or
LOSE for Temple.
Success (p)
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