probability

Esther Gruenhut, Jan 21, 2017

Table of Contents

  1. Bertrand Paradox
    1. Bertrand Paradox - First Method
    2. Bertrand Paradox - Second Method
    3. Bertrand Paradox - Third Method
    4. Bertrand Paradox - all in one

1.

Bertrand Paradox

Given a Circle, What is the probability to draw a chord longer than the length of an equilateral triangle inscribed in the circle. בהנתן מעגל, מה ההסתברות לבחור באקראי מיתר שאורכו גדול יותר מאורך צלע של משולש שווה צלעות החסום במעגל.

  • 1. Bertrand Paradox - First Method
  • 2. Bertrand Paradox - Second Method
  • 3. Bertrand Paradox - Third Method
  • 4. Bertrand Paradox - all in one

1.1.

Bertrand Paradox - First Method

Given a Circle, What is the probability to draw a chord larger than the length of an equilateral triangle inscribed in the circle.
Method I - All chords through given point on circle
Seems like the answer should be [math]\frac{1}{3}[/math].[br][br]This is not the only method of solving this problem. [br]Here is a [url=https://beta.geogebra.org/m/W3av3g5n#material/JrtK9W3q]link [/url] to a second method, and [url=https://beta.geogebra.org/m/W3av3g5n#material/bqECsYGV]here [/url]to a third. [br]
– Esther Gruenhut

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