It’s an irresistible news twist on an already intriguing story: First came the national news coverage of a huge lottery jackpot, a staggering $590 million. Then came the mystery when the winner did not come forward; days and weeks passed before 84-year-old Gloria Mackenzie of Zephyrhills, Fla., finally claimed her prize to become the largest sole lottery winner in history.
But the latest twist came when Mackenzie suggested that her ticket had been destined for someone else. According to an ABC News story,
Crandell said that she was using this incident as a lesson to her daughters about the importance of doing the right thing.
It’s good that Crandell has no regrets about allowing Mackenzie in front of her, since there’s no reason for regrets: the winning Powerball lotto probably would not have gone to her anyway.
Destiny or Random Chance?
The reason is that each Quick Pick number drawing is random and independent. That is, the numbers that are generated on a particular draw have nothing to do with the numbers that are generated before or after it.
Mackenzie could not have purchased the lotto numbers destined for Crandell; it’s not like the 540,003rd person who buys a lottery ticket would necessarily get those winning numbers; it could just as easily have been the 540,004th person.
Statistically, Crandell — as the person behind Mackenzie in line — had just as much chance of getting the winning numbers as the person ahead of Mackenzie, and the two-thousandth person after Mackenzie. Thus Mackenzie did not end up with the ticket destined for Crandell.
Though I have a pretty good grasp of probability, I’m not a statistician and so I wondered if I was missing something. John Allen Paulos, a professor of mathematics at Temple University and author of several best-selling books about statistics including “Innumeracy: Mathematical Illiteracy and Its Consequences” and “A Mathematician Read the Newspaper,” told me, “Yes, I think you’re right. The numbers are independently generated unless the buyer requests her own. Moreover, there is no reasonable metric according to which two tickets were ‘close’ or ‘almost’ winners.”
(Mackenzie chose a Quick Pick, but some superstitious players use specific numbers, such as their birthday, or their license plate numbers; in those cases the digits on the lotto tickets are not randomly generated, though the winning numbers are.)
So while the kind-hearted stranger who lost half a billion dollars in a kind act is a tantalizing footnote in this human interest story (and a morality lesson for Crandell’s daughters) the real lesson here is that statistics and probability — not acts of kindness — explain who wins the lottery.