In American Football, touchdowns are worth 6 points. After scoring a touchdown,
ID: 3153400 • Letter: I
Question
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 pts to the Killen Tigers near the end of regulation time. The only way for Temple to win (or tie) this games is to score two touchdowns while not allowing Killen 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 edn of regulation time, the game goes into overtime. The Temple coach believes that there is a 50% chance that Temple will win the game if they go into overtime. The probabliltiy of successfully converting a 1-pt. conversion is 1.0 the probabiliyt of successfully converting a 1 pt conversion is "p" .
QUESTION
Assume that a win results in a value of 1.0 and lose results in a value of 0. Further, assume that the probability of converting a 2 pt. conversion is p=0.4. Should Temple's coach go for a 1-pt conversion or 2-pt. conversion after scoring the first touchdown?
Explanation / Answer
For Temple to win there are three possibilities,
1)To score two touchdowns-12 points+2 1pt =14 points->draw+50% probability of winning in over time
2)To score two touchdowns-12pts+1 pt +2 pt=15 points->win
3)To score two touchdowns-12pts+2 pt=16 points->win
Lets calculate the probability of winning in each case:
1)Probability=1*1*0.5=0.5
2)Probability=1*0.4*2 =0.8
3)Probability=0.4^2 =0.16
But if we see after the first touchdown,
Probability to win if i take a 1 point->0.5+0.4 =0.9
Probabiltiy to win if i take 2 point->0.4*(1+0.4*0.5)+0.6*(0.4*0.5)=0.6
Hence there is a more probability to win if i take the 1 point in the first attempt.