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**CaptainBlack** Assume that in a period of 6 months that the incidence is either 0.0001 or 0.00015 and does not change during the six months.

The number occurrences in each case is (approximately) a Poisson random variable with expected numbers of occurrences of 3 and 4.5 respectively per month.

For wrongly reporting H we assume that the true expected number of occurrences per month is 3 and use the Poisson distribution to calculate the probability p(5+) that in any given month 5 or more occurrences are reported.

Now the number of months in our six month window for which 5 or more occurrences are reported is a Binomially distributed random variable ~B(6,p(5+)). So the probability of wrongly reporting H is:

P = b(3;6,p(5+)) + b(4;6,p(5+)) + b(5;6,p(5+)) + b(6;6,p(5+))

CB