Xi'an's Og

A riddle from The Riddler on cutting a square (toast) into two parts and keeping at least 25% of the surface on each part while avoiding Bertrand’s paradox. By defining the random cut as generated by two uniform draws over the periphery of the square. Meaning that ¼ of the draws are on the same side, ½ on adjacent sides and again ¼ on opposite sides. Meaning one has to compute

P(UV>½)= ½(1-log(2))

and

P(½(U+V)∈(¼,¾))= ¾

Resulting in a probability of 0.2642 (checked by simulation)

This entry was posted on November 25, 2022 at 12:22 am and is filed under Books, Kids, pictures, Statistics with tags Bertrand's paradox, chord, conditioning, Joseph Bertrand, measure theory, Monte Carlo experiment, riddle, simulation, slice, tartine, The Riddler. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.