Consider the lottery described in given exercise.
(a) Assuming six million tickets are sold and that each player selects his/her number independent of all others, find the exact probability of fewer than 3 players winning the lottery.
(b) Approximate the probability in part (a) using the Poisson approximation to the binomial distribution. (c) Approximate the probability in part (a) using the central limit theorem. In this example, which approximation is more accurate?
Exercise
In a certain lottery, six numbers are randomly chosen from the set 
(without replacement). To win the lottery, a player must guess correctly all six numbers but it is not necessary to specify in which order the numbers are selected.
(a) What is the probability of winning the lottery with only one ticket?
(b) Suppose in a given week, 6 million lottery tickets are sold. Suppose further that each player is equally likely to choose any of the possible number combinations and does so independent of the selections of all other players. What is the probability that exactly four players correctly select the winning combination?
(c) Again assuming 6 million tickets sold, what is the most probable number of winning tickets?
(d) Repeat parts (b) and (c) using the Poisson approximation to the binomial probability distribution. Is the Poisson distribution an accurate approximation in this example?