Congratulations to Pedro Quezada, the Dominican immigrant who just won $338 million in the Powerball Lottery. How about THAT for a piece of the American Dream?
In every Powerball, drawing resides the potential for hitting a big jackpot, but again there may not be a big winner at all. There are no guarantees.
We could discuss the fact that some people get carried away buying tickets with buying tickets they can’t afford, or we could talk about how states use the money to fund education and other worthy projects, but that’s no fun.
Most people when they think about the lottery contemplate winning and engage in a bit of generally harmless fantasy regarding the things they could buy and the good they could do for other with the money. But the question on the mind of anyone who spends two bucks for a ticket is, "What are my chances of winning all that money?"
Whenever the Powerball Jackpot starts to get high, people, (including me), buy a ticket, and hope for the best. Some people have special numbers, or a “foolproof” system to win. I am sad to report after considerable fiddling with the math that the very best “foolproof “system to guarantee lottery wealth is to write a book about your foolproof system and sell it to the hopeful, because the mathematics are generally unaffected by plans or systems that are possible to operate within the finances of 99% of lottery players. Your odds of winning don’t change whether they sell one million tickets or one billion tickets. The only thing that changes is the size of the jackpot and the probability of having to split the money with someone who picked the same numbers.
As I noted before, everyone is of course interested in how to determine his or her chances of winning. Of course, one could go to the Powerball FAQ page and just look up their probability of winning, but what fun would that be.
Under the current Powerball Lottery rules, one must select a 5 number combination out of 59 possible numbers that may not be repeated. Then they must select the “Powerball” itself from a range of 35 numbers and combine it with the first five to obtain their winning guess.
There are two ways to determine the possible number of combinations. The first way is to calculate the possibility of selecting the first number and combing the result with the probabilities of selecting each subsequent number by doing some complicated calculations and fraction conversions or you can do as I did and use the COMBIN function in Microsoft Excel to calculate the number of possible combinations where the first number in the parentheses represents the number of possible choices and the second number represents the number of choices allowed.
=COMBIN(59,5) equals 5,006,386
=COMBIN(35,1) equals 35
5,006,386 X 35 equals 175,223,510
So the probability of hitting the Powerball Big Jackpot with the purchase of a single ticket is 1 in 175,223,510. In case you haven’t check, this is the same number you will find on the Powerball FAQ page. Ta Da!
One can change ones odds by purchasing more tickets, but one would have to spend a lot of money in order to significantly increase one’s probability of winning. Since tickets cost $2.00, if one spent $100.00 on tickets they would increase their probability of winning to 1 in 3,504,470.2. But when one purchases more tickets, it also increases the probability that someone else will select the same numbers resulting in a split pot.
Do I strongly believe that I am at all likely to hit the big jackpot? No, of course not, because I have a basic understanding of the mathematics involved. Nevertheless, when I purchase my occasional one ticket I look at it as a gamble, a small investment with a very slight chance for yielding immense financial reward. I knowingly take a chance on winning a life changing amount of money for less than the cost of a trip through the drive-thru at the Golden Arches.
We all need a break from the Second Amendment, the Supreme Court, and politics as usual. I’d like to invite all of you to join me in a game of Comparative Probability. To play, all you have to do is figure a comparative probability and report what lesson can be learned from the comparison.
I’ll go first. The odds of getting struck by lightning have been calculated at one in 2,000,000, which makes a person 88 times more likely to get struck by lightning than win the big Powerball jackpot.
Lesson: Don’t go out in a storm to buy your lottery ticket.
Please join in by posting your probability in the comments section.