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5. Random pigeonholing

100 pigeons p1,…,p100 fly into 500 labelled holes h1,…,h500. Each pigeon picks a hole uniformly at random and independently from the choices of the other pigeons.

  1. What is the probability that at least one hole contains at least 2 pigeons.
    Hint: The answer is approximately 0.9999758457295991
  2. What is the probability that at least one hole contains at least 3 pigeons.
    Hint: The answer is approximately 0.4361298523736379.5. Random pigeonholing 100 pigeons P1,...,P100 fly into 500 labelled holes h1,...,h500. Each pigeon picks a hole uniformly at
math   Statistics-And-Probability   
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Answer #1

DConside he above given ha total Pigeons = 100 -hso o labelled holes = Soo * Ae finst pigons has a loo chance of jeHing of ume20 sdshte at (ea2s0) EVc00) He Pobabih hat at least one hole Contains at least 2 Pigeons -1/sc0 (elecal 7 O.998001999/ the P

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