• The following table is based on data from Helmet Use and Risk of Head Injuries in Alpine Skiers and Snowboarders, by Sullheim, et al., Journal of the American Medical Association, Vol. 295, No. 8).

	Head Injuries	Not Injured
Wore Helmet	96	656
No Helmet	480	2330

• If one of the subjects is randomly selected, find the probability of selecting someone with a head injury.
  • If one of the subjects is randomly selected, find the probability of selecting someone who wore a helmet.
  • If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet or was not injured.
  • If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet and was not injured.
  • If two different study subjects are randomly selected, find the probability that they both had head injuries.
  • If one of the subjects is randomly selected, find the probability of selecting someone who was not injured, given that the subject wore a helmet.
• In a basketball arena,
• 70% of the fans are rooting for the home team.
• 25% of the fans are wearing blue.
• 20% of the fans are wearing blue and are rooting for the away team.
• Of the fans rooting for the away team, 67% are wearing blue.
  • Are the events of wearing blue and rooting for the away team independent? How do you know?
  • Are they mutually exclusive? How do you know?
• Use counting rules to answer the following problems.
  • Find the number of different ways that the nine players on a baseball team can line up for the National Anthem.
  • A political strategist must visit state capitols, but she has time to visit only 3 of them. Find the number of different possible routes.
  • A statistics professor owns a safe in which he stores all of his great ideas for the next edition of his textbook. The safe combination consists of four different numbers between 0 and 99. If another author breaks in and tries to steal these ideas, what is the probability that he or she will get the correct combination on the first attempt? Assume that the numbers are randomly selected.
  • How many 5-card draw poker hands are there? In other words, in how many ways can I select 5 cards from a deck of 52 cards, where the order in which they are dealt doesnt matter?
  • The Florida Lotto game is typical of state lotteries. You must select six different numbers between 1 and 53. You win the jackpot if the same six numbers are drawn in any order. Find the probability of winning the jackpot.
  • In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Find the number of different possible trifecta bets in a race with ten horses.

EXTRA CREDIT:

• Suppose you own a sports-themed burger shop called The Yard. It is very popular with the local high school, St Matthews School for Boys. However, it is even more popular now that your new employee for the summer, Kelli, has started making her famous chocolate milkshakes for your customers. Youve estimated that when a potential customer walks by and sees that Kelli is working, 9 times out of 10 they come in for a milkshake. A group of 4 students from St Matthews have just gotten off the bus.
  • Assuming that each student thinks independently, what is the probability that Kellis milkshake brings all the boys to The Yard?
  • It is probably not a good assumption that teenage boys think independently of each other. Assume instead that if any boy chooses to come, they all do. Now what is the probability that Kellis milkshake brings all the boys to The Yard?