Question 1: In the well known game of TattsLotto, the winning numbers are six number selected without replacement from forty ve numbers, ie., 1,2, . . . ,45. Two supplementary numbers are also selected without replacement. Each ticket purchased consists of six numbers and it wins a money prize if these numbers fall into any one of the following six divisions. A higher division will pay more money than a lower division. The divisions are: Division 1: six winning numbers; Division 2: ve winning numbers plus one number from two supplementary numbers; Division 3: ve winning numbers; Division 4: four Winning numbers; Division 5: three winning numbers plus one or two supplementary numbers; Division 6: one or two winning numbers plus two supplementary numbers. (a) Find the probability of winning a prize in each division with the purchase of a single ticket. (b) What is the odds of Winning a prize? (Note: the odds of an event A PgA) ) occurring is equal to the ratio 1,?(A) (c) If each ticket costs $1, how many tickets should be purchased to get an expected return of $1000? (d) If you have bought $1000 tickets, what is the probability of winning a prize? (Hint: use the Poisson approximation to the binomial distribution, ie.; if n is large and p is small, then a binomial distribution (71,10) can be approximated by a Poisson distribution with mean up.)