Bertrand's Paradox
Presented by Eugene Kang
Problem
What is the probabilit y of a random chord of
a unit circle having a length greater th an 3,
the side of an inscribed equilatera l triangle?
A chord of circle – line segment from a point
on the circle to another point on the circle
Answer Choices
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A.
2
1
B.
3
1
C.
4
Mathematical Solutions
Parallel Slices
Mathematical Solutions
Angle Slices
Mathematical Solutions
Random Slices
ftp://ftp.haverford.edu/pub/cgreene/prob/text/bookprograms
/chap2/BertrandsParadox.Chpt2.mat.nb
Bertrand's Paradox for Dummies
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Not to be Confused
• Bertrand’s Paradox vs. Bertrand Paradox
Credit
• http://web.mit.edu/tee/www/bertrand/
• Charles M. Grinstead, J. Laurie Snell,
INTRODUCTION TO PROBABILITY
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html
• http://www.cut-the-knot.org/bertrand.shtml