Answer:
(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:
[tex]D= \frac{t_D}{t_D+t_M}= \frac{2}{2+6}\\D= \frac{1}{4}=0.25[/tex]
(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:
[tex]D_{TD}=\frac{time\ of\ possession}{time\ per\ possession} *P(TD)} \\D_{TD}=0.25*\frac{60}{2}*\frac{1}{4} \\D_{TD}= 1.875\ TDs\ per\ hour[/tex]
The number of TDs per hour scored by Miami, on average, is:
[tex]M_{TD}=\frac{time\ of\ possession}{time\ per\ possession} *P(TD)} \\M_{TD}=0.75*\frac{60}{6}*1 \\M_{TD}= 7.5\ TDs\ per\ hour[/tex]
