Testing Buridan

Discrete Mathematics Level pending

The French philosopher Buridan once stated that "A hungry jackass, placed at an exactly equal distance between two identical piles of hay, will starve to death, as it will have no reason to select one pile over the other."

A wealthy rancher who dabbled in philosophy and mathematics decided to put Buridan's hypothesis to the test. He had 10 ramps constructed, each of which led to the exact center of a platform where on either side, two identical piles of hay were placed at an exactly equal distance. He then purchased 10 jackasses (Gohmert, Poe, Johnson, Ratcliffe, Hensarling, Barton, Culberson, Brady, McCaul and Conaway) and gave them only water for 16 hours to make sure they were good and hungry. Then each jackass was led down the ramp to the center of the platform.

Not a single one of the jackasses froze in place and starved to death, thus disproving Buridan's hypothesis.

If the chance of each jackass going to the left pile of hay is identical to the chance it will go to the right pile of hay, what are the chances that exactly 5 jackasses go each direction? Give answer in percent to 2 decimal places.

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