One state lottery game has contestants select 5different numbers from 1 to 45. The prize if all numbers arematched is 2 million dollars.  The tickets are $2each.

Please show work.

1)    How many different ticket possibilities arethere? Hint: use combinations here 45 C 5.  Order of thenumbers doesn't matter, just matching them, so we don't needpermutations.  

2)    If a person purchases one ticket, what isthe probability of winning? What is the probability of losing?

3)    Occasionally, you will hear of a group ofpeople 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 tocontribute?

b)    What is the probability of the groupwinning? Losing?

4)    How much would it cost to “buy thelottery”, that is, buy a ticket to cover every possibility? Is itworth it?

5)    Create a probability distribution table forthe random variable x = the amount won/lost when purchasing oneticket.

6)    In fair games, the expected value will be$0. This means that if the game is played many…many times, then oneis expected to break even eventually. This is never true for Casinoand Lottery games.   Find the expected value of x = theamount won/lost when purchasing one ticket.

7)    Interpret the expectedvalue.  

8)    Fill in the following table using theexpected value.

Number of tickets purchases	Expected net winnings for the lottery	Expected net winnings of a fair game (expected value =0)
100,000		$0
500,000		$0
1,000,000		$0
5,000,000		$0