Page 157 - Probability Demystified

146 CHAPTER 8 Other Probability Distributions

6 numbers from the numbers 1 to 49. If the player matches all six numbers,
the player wins a minimum of $500,000. (Note: There are other ways of
winning and if there is no winner, the prize money is held over until the next
drawing and increased a certain amount by the number of new players.)
For now, just winning the $500,000 will be considered. In order to figure the
odds, it is necessary to figure the number of winning combinations. In this
case, we are selecting without regard to order 6 numbers from 49 numbers.
Hence there are 49 C 6 or 13,983,816 ways to select a ticket. However, the odds
given in the lottery brochure are 1 : 4,661,272. The reason is because if you
select 6 numbers, you can have the computer select two more sets of six
numbers, giving you three chances to win. So dividing 13,983.86 by 3, you
get 4,661,272, and the odds are 1 : 4,661,272.
Now let’s make some sense of this. There are 60 seconds in a minute,
60 minutes in an hour and 24 hours in a day. So there are 60 60 24 ¼
86,400 seconds in a day. If you divide 4,661,272 by 86,400, you get app-
roximately 54 days. So selecting a winner would be like selecting a given
random second in a time period of 54 days!
What about a guaranteed method to win the lottery? It does exist. If you
purchased all possible number combinations, then you would be assured of
winning, wouldn’t you? But is it possible?
A group of investors from Melbourne, Australia, decided to try. At the
time, they decided to attempt to win a $27 million prize given by the Virginia
State Lottery. The lottery consisted of selecting 6 numbers out of a
possible 44. This means that they would have to purchase 44 C 6 or 7,059,052
different tickets. At $1 a ticket, they would need to raise $7,059,052.
However, the profit would be somewhere near $20 million if they won. Next
there is always a possibility of having to split the winnings with other
winners, thus reducing the profit. Finally, they need to buy the 7 or so million
tickets within the 72 hour time frame. This group sent out teams, and they
were able to purchase about 5 million tickets. They did win the money
without having to split the profit! Some objections were raised by the other
players (i.e., losers), but the group was eventually paid off.
By the way, it does not matter which numbers you play on the lottery since
the drawing is random and every combination has the same probability of
occurring. Some people suggest that unusual combinations such as 1, 2, 3, 4,
5, and 6 are better, since there is less of a chance of having to split your
winnings if you do indeed win.
So what does this all mean? I heard a mathematician sum it all up by
saying that you have the same chance of winning a big jackpot on a state
lottery, whether or not you purchase a ticket.