I would use an exponential decay equation (video here: https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/exponential-decay-alg1/v/exponential-decay-intro). 

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I would approach the problems by using a binomial distribution (more info here: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library/binomial-random-variables/v/bi...

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