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A lake contains g gudgeon and r roach. You catch a sample of size n, on the understanding that roach are returned to the lake

A lake contains g gudgeon and r roach. You catch a sample of size n, on the understanding that roach are returned to the lake after being recorded, whereas gudgeon are retained in a keep-net.

  1. Find the probability that your sample includes k gudgeon.

  1. Show that as r and g increase in such a way that g/(r + g) p, the probability distribution tends to the binomial.

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