Philip Ernst, assistant professor of statistics at Rice University, is available to comment on tonight’s $1.5 billion Powerball drawing.
The current odds of winning the jackpot are 1 in 292,201,338. What is the math behind it?
“The game has five white balls labeled from 1 to 69 and one red ball labeled from 1 to 26,” Ernst explained. “By the counting rule from elementary probability theory, this gives (69 times 68 times 67 times 66 times 65 times 26) equals 35,064,160,560 — or about 35 billion — possibilities for the exact sequence of numbers to be drawn for the jackpot.”
“However, since a winning ticket can have the white numbers listed in any order, one needs to divide this number by 5 factorial (120), and thus 35,064,160,560 divided by 120 equals 292,201,338 (or about 292 million). This is how they get the number on their website, although it would be nice — at least for us statisticians! — if people understood the calculation.”
Why not buy all the combinations to guarantee a jackpot winner?
If one person bought all 292,201,338 possible tickets, that person would be guaranteed of winning the jackpot,” Ernst said. “However, since each ticket costs $2, this strategy would cost someone $584,402,676. The cash value of today’s jackpot (if one chooses the lump sum) is $930 million. If you are taxed on the winnings at 50 percent, you would end up with $465 million, meaning you’d end up losing a whopping $119,402,676. You would lose much more if another person also has a winning ticket and the prize is split!”
According to Ernst, you are more likely to:
Be struck by lightning than to win the jackpot. According to the National Weather Service, the likelihood of being hit by lightning is 1 in 1,190,000 — or about 245 times more likely than winning the jackpot.
Die in a plane crash than to win the jackpot. A person’s chances of dying in a plane crash are reported to be 1 in 11 million — or about 26 times as likely as winning the jackpot.
If no one wins the jackpot tonight, the next drawing will balloon to more than $2 billion.