A Penchant for Perfection
An amateur golfer from Stockton, California recently made local headlines  by sinking his 16th career hole-in-one at a tournament in Reno. Rod Souza Sr., a 60-year old retired Fire Department Captain attributes his success to two things: "frequency of play and luck". According to Golf Digest, the odds of an amateur golfer hitting a hole-in-one on a given hole are 1 in 12,750.
1) In the article, Mr. Souza tells reporters that he has been playing golf for over 40 years, averaging 3-4 rounds per week during this time. Suppose that he averages 3.5 rounds per week and that a round consists of 18 holes. If Mr. Souza was relying on "luck" alone, how many hole-in-ones should he expect to have after 40 years of playing golf?
2) What is the probability that Mr. Souza would have made 16 or more hole-in-ones if he was relying on chance alone?
3) Based on your calculation in question 2, do you think Mr. Souza has shown an unusually high "penchant for perfection"?