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To answer this question, we shall apply the Negative Binomial distribution.
Let contracting the disease be considered a "success". The number of success is what we are interested in.
Let be the sample size of the sample until we get 2 successes. The probability of contracting the disease is . The form of the Negative Binomial distribution we apply is given as,
Therefore, the probability that 8 mice are required is 0.0651