How many people do you have to meet to have a 50% chance somebody has Covid at an incidence of 500 (in 100k people)

_Readme.md

This is a simulation we wrote to understand whether ln(1-0.5) / ln(1-500/100000) is the right formula to apply here.

Incidence.hs

module Main where

import System.Random
import Data.Ratio
import Data.Bifunctor

-- | Returns for a bunch of people you meet , with a chance of 1/200 for each person, whether any has Covid
randomPeople200 :: (RandomGen gen) => Int -> gen -> (Bool, gen)
randomPeople200 numberOfPeople =
 first anyHasCovid . runGeneratorNTimes numberOfPeople 0 (uniformR (1, 200::Int))

anyHasCovid :: [Int] -> Bool
anyHasCovid = any (== 1)

runGeneratorNTimes :: (RandomGen gen) => Int -> a -> (gen -> (a, gen)) -> gen -> ([a], gen)
runGeneratorNTimes times ignored f gen = do
  let (gen1, genRes) = split gen
  (map fst . take times . drop 1 $ iterate (\(_old, gen) -> f gen) (ignored, gen1), genRes)


percentage ls = realToFrac (100 * (length (filter (==True) ls) % length ls))

main = do
  gen <- newStdGen
  print $ fst $ randomPeople200 15 gen
  print $ percentage $ fst $ runGeneratorNTimes 1000 False (randomPeople200 138) gen