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

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

Question 1. (10 Marks in total). 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. (4 Marks in total) 2. Show that as r and g increase in such a way that g/ (g + r) - p , the probability distribution tends to the binomial.(6 Marks in total)