# Do I have more chances to get struck by lightning or to win at the lottery

Very small/classical question.

If you are European fellows you for sure know that the European lottery, named EuroMillions is "offering" today something around €125,000,000.

Damn, that's a pretty nice amount, and for once I realized that I should perhaps give it a try, a simple ticket is only about 2€. But then even for 2€, does it really worth it, or do I have more chance to get struck by lightning ?!

As explained on Wikipedia link, a single grid is composed of 50 "classical" numbers & 11 stars (numbered from 1 to 11). You have to select 5 numbers & 2 stars per grid.

I know this is an old fashion question, but from what I have read here, I would be very interested to hear more about what you, gentlemen, are thinking of this.

Probabilities to become a strike lightning survivor, and/or multimillionaire strike lightning survivor would be some nice to have :)

*Update, after the lottery *: I forgot one value ... the fact that on the lottery day, you can go back home too late to be able to buy a ticket, no matter what's the weather looks like.

And to be honest, the sky was very nice yesterday with no clouds, and no lightning at all, but I was not able to buy a ticket and to play the lottery, so it makes easier the computation of winning chances ;)

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We're not all gentlemen. Some of us are actually pretty un-gentle... – user1729 Sep 6 '11 at 11:55
Do you want to calculate the probability of winning, or do you want something else? – Srivatsan Sep 6 '11 at 12:24
@Srivatsan, thanks ... but if you check from the Wiki link I already provided, the probability of winning are already there, and from my small knowledge it looks like (50! - 45!)/(5!) * (11! - 9!)/(2!) – Sebastien Thuilliez Sep 7 '11 at 5:34
So what do you want? Statistics on lightning strikes? If so, this is the wrong place to ask. – Peter Taylor Sep 7 '11 at 9:07

It's a little easier to think about buying a certain number of tickets each year. So let's say you buy one ticket each year (great birthday present!).

Your profile uses a Swiss LinkedIn link, so I'll assume you're living in Switzerland. The population of Switzerland is about 8 million. If only one person were struck by lightning each year in Switzerland, you could naively say your probability of being struck by lightning is $\frac{1}{8,000,000}$. The EuroMillions Wikipedia article says that the odds of winning the jackpot are more like $\frac{1}{116,000,000}$. So you're about 15 times as likely to be struck by lightning!

To get the probability of both winning the jackpot and being struck by lightning, multiply the two individual probabilities together.

This is a simplified calculation: things get a little more complicated if you buy more than one ticket, and I'm assuming that you don't run in around in rainstorms with a tall, iron pole. The calculation of the probability of winning and being struck assumes that the two events are independent, that being struck by lightning doesn't affect your odds of winning the lottery, and vice-versa.

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What's the probability that you win the lottery and then get struck by lightning before you get to collect your winnings ? – Paul R Sep 6 '11 at 12:34
@Paul R. pretty nice one, I missed it ! – Sebastien Thuilliez Sep 6 '11 at 13:00
I assumed one could win posthumously. – Adam Saltz Sep 6 '11 at 19:45
How does the probability of getting struck by lightning while you are on your way to buy a ticket compare to the other probabilities that were mentioned above? Is the expected cost of medical bills in this instance higher than the expected earnings from a lottery ticket? – Jay Sep 6 '11 at 20:09
@Brian, +1 for the deep search on my profile ;) – Sebastien Thuilliez Sep 7 '11 at 5:39

According to NOAA, roughly 1 in 600,000 people dies by lightning strike is struck by lightning in the US every year. (Thanks to Steven Stadnicki for pointing out that NOAA doesn't say they all die.) Conveniently, the Wikipedia page you link to computes the odds of winning Euromillions at 1 in 116,531,800 -- about 200 times worse!

Since you probably will feel cheated to come to a math site and not see a computation, the number of ways to choose 5 numbers out of 50 is $$\frac{50 \times 49 \times 48 \times 47 \times 46}{5 \times 4 \times 3 \times 2 \times 1}$$ and the number of ways to choose $2$ numbers out of $11$ is $$\frac{11 \times 10}{2 \times 1}.$$ Presumably, the product of these two is 116,531,800.

Even without doing the computation, notice that Euromillions is offering a € 125,000,000 payout for a € 2 fee. So it is safe to assume that the odds of winning Euromillions are less then 1 in 62,500,000. This is an easy way of getting an upper bound on the odds of winning any lottery -- if the bet were in your favor, why would the government be offering it?

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Many lotteries in the US carry over some of the money if the jackpot is not won. In that case, it can be mathematically advantageous to play when the carryover is large even though the government makes money. However, we see lots of tickets sold in those cases, so the prize will likely be divided, which reduces your odds... – Ross Millikan Sep 6 '11 at 14:37
@David, +1 for the link from NOAA. But I hope, I will be able to survive from the lightning strike here, so I guess the values to take into account are : Average number of lightning strikes worldwide every second - 100 or Average number of lightning strikes worldwide per day - 8.6 Million ... damn that's huge ! – Sebastien Thuilliez Sep 7 '11 at 5:38
Your NOAA citation is incorrect, actually - note that they say that the average per capita strike rate is 1 per 600,000, but not every strike is fatal; in fact, guessing from the statistics above that it seems like roughly one in every four lightning strikes is fatal. Not that this substantially changes the comparative statistics, of course, but it's a distinct difference... – Steven Stadnicki Sep 7 '11 at 6:24