Question

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.

Please show work.

1)    How many different ticket possibilities are there? Hint: use combinations here 45 C 5.  Order of the numbers doesn't matter, just matching them, so we don't need permutations.  

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

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?

b)    What is the probability of the group winning? Losing?

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

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 $0. This means that if the game is played many…many 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.

7)    Interpret the expected value.  

8)    Fill in the following table using the expected 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

Answer 1