Statistically Speaking, with Dr. Gadbois

Simpson’s Paradox. Buffon’s Needle. The Gambler’s Fallacy. Dr. Steve Gadbois, instructor in math, piqued students’ interest in probability and statistics this week during an intriguing chapel presentation. 
Using concrete examples such as batting averages in baseball, card shuffling, coin flipping, and poker with wild cards (a topic which landed him an interview on NPR’s “All Things Considered” exactly 21 years earlier), Dr. Gadbois presented several challenges that involve the calculation of probabilities. He emphasized how important it is to consider the exact wording of the problem in arriving at the correct answer. Consider these questions:

(1) Which is more likely, getting at least one six in four throws of one die, or at least one pair of sixes in 24 throws of two dice?
(2) How many people need to be in a room before the chance of at least one repeated birthday reaches 50 percent?
(3) Does 2+2 really equal 4?
(See answers below.)
 
He also shared some real-world situations in which the use of probability and statistics has more serious import, such as in earthquake predictions, proper use and understanding of false positive or negative results on medical tests, and the operation of the draft lottery conducted in the early ’70s to determine military service in the Vietnam War.  
 
MUS has three instructors with advanced degrees in statistics – Dr. Gadbois, Mr. Darin Clifft, and Mr. Phillip Stalls. Calling probability and statistics a favorite subject, Gadbois said it is one of the most important math classes the school offers, and he encouraged students to come talk to him or his colleagues if they wanted to better understand the challenges he presented.
 
“If you don’t believe my examples, come talk to me or Mr. Clifft or Mr. Stalls. Everything I tell you today is true!”
 
Answers
(1) The first event is slightly more likely (52% to 49%)
(2) 23
(3) Three-fourths of the time it does (at least for scientists) 
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