One state lottery game has contestants select 5 different numbers from 1 to 45. the prize if all numbers
are matched is 2 million dollars. the tickets are $2 each.
1) how many different ticket possibilities are there? 45c5 =1,221,759
2) if a person purchases one ticket, what is the probability of winning?
1 in 1,221,759 = .8184920267
what is the probability of losing?
1-.8184920267 = .54906
3) occasionally, you will hear of a group of people going in together to purchase a large amount of
tickets. suppose a group of 30 purchases 6,000 tickets.
a) how much would each person have to contribute? 6000/30 = 200 tickets per person at $2 per
ticket = 200(2) = $ 400 per person.
b) what is the probability of the group winning? 6000/1221759=0.004910952
losing? 1-0.004910952 = .995089048
4) how much would it cost to "buy the lottery", that is, buy a ticket to cover every possibility? is it
worth it? 2(1221759) = $2,443,518
5) create a probability distribution table for the random variable x = the amount won/lost when
purchasing one ticket.
6) in fair games, the expected value will be $o. this means that if the game is played
times, then one is expected to break even eventually. this is never true for casino and lottery
games. find the expected value of x = the amount won/lost when purchasing one ticket.