Probability Wonders
From now on, the NCTM Newsletter will include a Problem to Ponder personally selected by NCTM President Mike Shaughnessy. Here's the first one concerning simple probabilities.
Does It Matter Which Winner You Saw?
Scenario: Students at your school have just finished competing in the qualifying round of a nationally sponsored contest on mathematical reasoning and sense making. When the work was scored, it turned out that four students at your school all had perfect preliminary papers—two girls and two boys. The school decided to hold a random drawing among these four students to select two of them to send to the national finals. The drawing takes place in the school auditorium. You show up late to the drawing, just as one of the winners—a girl—is leaving the stage amid cheers.
- Suppose that the girl that you saw leaving the stage is the first winner. What is the probability that the second winner will also be a girl?
- Suppose that the girl that you saw leaving the stage was the second winner. What is the probability that the first winner was also a girl?
There is a third scenario wherein you only peek into the auditorium, see a girl, but have no idea whether she's the first or the second selection.
As we learn from an article in the NewScientist, at the latest Gathering for Gardner, Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle gave a remarkably short talk. It consisted of the following three sentences: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"
How does it change the solution of a well known problem to know that one of the boy was born on Tuesday? What difference does it make which day he was born on?
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[...] an early June issue of the NCTM newletter, President Mike Shaughnessy offered a Problem to Ponder: Scenario: Students at your school have just finished competing in the qualifying round of a [...]
July 15th, 2010 at 1:05 pm