Question: Initially a box is empty. In each step, we put one blue ball and Poisson(1) many red balls in the box, independently of all other

Initially a box is empty. In each step, we put one blue ball and Poisson(1) many red balls in the box, independently of all other steps. Let Pn be the proportion of blue balls in the box after n steps. Show that if n31 then Pn10/21 with probability approximately at most 1/1000. Fully justify your answer.

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