Abetting company wishes to sell 5000 tickets 50 of which will win prizes. i.) a students decided to buy 200 tickets. let x be the number of tickets that win a prize. write the probability distribution of x and give its mean. ii.) using a poisson approximation for the distribution of x find the probability of at least three tickets winning a prize. iii.) calculate the number of tickets that should be bought so as the probability of at least one winning a prize is 90%