The number of injuries at a college football game has the following probability distribution:
Probability 0.14 0.33 0.23 0.17 0.09 0.04 Number of injuries 0 1 2 3 4 5
The coach must file a report whenever there is more than one injury in any game.
Calculate the expected number of football games to be played before the first game in which there are at least four injuries.
$$\sum\limits_{n=0}^{\infty}n\cdot(1-0.09-0.04)^n\cdot(0.09+0.04)=6.69231$$