Find minimum n for probability condition

A question is this type if and only if it asks to find the smallest or largest value of n (sample size) such that a probability condition is satisfied.

1 questions · Standard +0.3

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CAIE S2 2021 June Q5
7 marks Standard +0.3
On average, 1 in 75000 adults has a certain genetic disorder.
  1. Use a suitable approximating distribution to find the probability that, in a random sample of 10000 people, at least 1 has the genetic disorder. [3]
  2. In a random sample of \(n\) people, where \(n\) is large, the probability that no-one has the genetic disorder is more than 0.9. Find the largest possible value of \(n\). [4]