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### Course: Wireless Philosophy>Unit 2

Lesson 8: Probability

In this Wireless Philosophy video, Jonathan Weisberg (University of Toronto) explains Bertrand's Paradox, a famous paradox in probability theory. Beginning with the square factory example, he talks about how Bertrand's Paradox reveals a puzzling problem for the principle of indifference and the implications of this paradox for scientific reasoning.

## Want to join the conversation?

• Sticking my head out and I am aware I may be absolutely wrong, but I think this approach may solve the paradox:

In my most humble opinion, the paradox arises due to, for instance, comparing apples with oranges, since we are comparing values in a linear range with values of a quadratic function. To compare like with like, think slope (1st derivative) of the quadratic curve for corresponding area values should be used.

The 1st derivative (slope) of the equation y = x^2 can be calculated as 2x. The corresponding values at relevant intervals can be calculated as follows:

for length x = 1, area = 1, and 2x = 2;
for length x = 2, area = 4, and 2x = 4;
for length x = 3, area = 9, and 2x = 6;

A: corresponding 2x range for interval x = 1 to 2, is 4 - 2 = 2;
B: corresponding 2x range for interval x = 1 to 3, is 6 - 2 = 4;
Therefore, corresponding probability of A / B can be calculated as 2 / 4 = 1 / 2 = same as the probability calculated for corresponding length range.