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.

1) How many different ticket possibilities are there?

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. See section 4.2 in the textbook for an example on how to 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

Please answer all questions! I will rate you!

Answer 1

1) Number of different ticket possibilities = = 1,221,759

2) For a purchase of one ticket, the probability of winning = 1/1,221,759 = 0.0000008185

The probability of losing = 1 - P(winning) = 0.9999991815

3)

(a) Each person would have to contribute $2*6000/30 = $400

(b) The probability of the group winning = = 0.00491

The probability of the group losing = 1 - 0.00491 = 0.99509

4) It would cost a total of $2*1,221,759 = $2,443,518 to buy the lottery

Since the cost to buy the lottery is greater than the prize, buying the lottery is not worth it.

5) The probability distribution table for x

x	$1,999,998	-$2
P(X = x)	0.0000008185	0.9999991815

6) Expected value of x =

= -$0.363

7) It is expected that the contestant loses $0.363 for each ticket he/she buys if the ticket is bought many times

8)

Number of tickets purchases	Expected net winnings for the lottery	Expected netwinnings of a fair game(expected value = 0)
100,000	-$36,300	$0
500,000	-$181,500	$0
1,000,000	-$363,000	$0
5,000,000	-$1,815,000	$0