A lottery has a very large number of tickets, one in every 500 of which entitles the purchaser to prize. An agent sells 1000 tickets for the lottery. Using a Poisson approximation, find, to three decimal places, the probability that the number of prize-winning tickets sold by the agent is

(a) less than three

(b) more than five. Calculate the minimum number of tickets the agent must sell to have a 95% chance of selling at least one prize-winning ticket. (NEAB)