Ask Dr. Knowledge

The odds of hitting the Mega Millions lottery?

May 18, 2009
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How likely am I to hit the jackpot in the Mega Millions lottery - and how do the odds compare with being hit and killed by lightning?

Quoting from the Massachusetts State Lottery website, here is how it works:

"Five balls are drawn from a set of balls numbered 1 through 56; one ball is drawn from a set of balls numbered 1 through 46."

To get the answer, we have to work out how many possible ways the lottery numbers can come out so you can see what your chances are if you play one number.

First we draw one ball, which can have any of 56 numbers. The next one is any of the remaining 55, the next is any of the remaining 54, and so forth. (For math fans, the calculation looks like this: 56 x 55 x 54 x 53 x 52 = 458,377,920.)

We then factor in that the order of the balls makes no difference. Any five numbers could be ordered in 120 ways (that calculation looks like this: 5 x 4 x 3 x 2 x 1 = 120 orderings), any of which would be OK to win.

So we divide 458,377,920 by 120, leaving 3,819,816 ways for the first five numbers to come up, disregarding the order.

The chance that the sixth ball - called the megaball and chosen from the separate batch of 46 - is right is 1 in 46. Factor in that probability (the calculation looks like this: 3,819,816 x 46) and that makes the odds of being the jackpot winner 1 in 175,711,536.

So how does that compare with the odds of being hit by lightning?

If you take the US population to be about 300 million and about 30 people per year get killed by lightning (it was actually 24 in 2008, according to the National Weather Service) then there's about a 1 in 10 million chance of being struck by a bolt from the blue.

And that is about 20 times higher than winning the big jackpot!

Dr. Knowledge is written by physicist John Swain of Northeastern University. E-mail questions to or write Dr. Knowledge, c/o The Boston Globe, PO Box 55819, Boston, MA 02205-5819.