In the duke versus miami football game, possessions alternate between duke who has the ball for an average of 2 minutes and miami who has the ball for an average of 6 minutes. (a) in the long run what fraction of time does duke have the ball? (b) suppose that on each possession duke scores a touchdown with probability 1/4 while miami scores with probability one. on the average how many touchdowns will they score per hour?

(a) 1/4 or 25% of the time

(b) Duke = 1.875 TDs/hour

    Miami = 7.5 TDs/hour

Step-by-step explanation:

(a) The fraction of time Duke has the ball is given by Duke's time of possession divided by the time it takes both teams to have a possession:

(b) If Duke has the ball for 25% of the time, Miami has the ball for the other 75%. The number of TDs per hour scored by Duke on average is:

The number of TDs per hour scored by Miami, on average, is: