## Probability Retake Test

### 5 points each for a maximum of 60 points, hence you can only achieve 60 of the 100 points which were possible on the inclass test

Questions are based on the roster you downloaded for the first retake test, if you did not take that test, you will need to download a roster.
1. What is the probability that a randomly chosen player is offense? defense? line? backfield?; Offense and backfield? offense or backfield? offense or defense? guard or tackle?
2. P(offense|line)=?, P(line|offense)=?, P(tackle|defense)=?. P(defense|tackle)=?, P(tackle|offense)=?
3. Give two categories of players that are complementary; give two categories of players that are mutually exclusive (disjoint), but not complementary; give two categories of players that are independent (this may not be possible - if that is the case, discuss); give two categories of players that are neither complementary, mutually exclusive, nor independent.
4. What are the points in the probabiity space? Which of the columns in the spreadsheet define random variables?
5. If all offensive backfield players can play any backfield position, how many different offensive backfields are there (teams of four, not distinguished positions)?
6. If all offensive backfield players can play any backfield position, how many different offensive backfields are there (four distinguished positions)?
7. If a kicker kicks in 20% of the games (and the chances of kicking in games are independent), in a given season, what is the probabiity that he kicks in 1, 2, 3, 4, ... games?
8. If the total duration of a game is normally distributed with mean 140 minutes and standard deviation 18 minutes, what is the probability that a game will last more than 2.5 hours? 3 hours?; how much time should they reserve for a game if they only want 4% of the games to run over the allotted time?
9. If 24% of college football players are seniors, what is the probability that fewer than 12 in a random group of 60 football players are seniors?
10. Using the mean and standard deviation of the weights from the team you chose, and assuming weights are normally distributed, what is the probability that a random choice of eight football players will weigh more than a ton?
11. If 1/3 of the cheerleaders are men with an average weight of 180 pounds and 2/3 of the cheerleaders are women with an average weight of 120 pounds, what is the average weight of the cheerleaders? (this is an expected value problem).
12. How many different ways can a pair of team members be chosen? If a pair of team members is randomly chosen, what is the probability that it contains at least one quarterback?
July 2014