## Another coincidence in lotteries

Here is a lottery story that appeared in the LA Times (and in numerous other journals and news reports):

On the television show Lost, the character Hugo “Hurley” Reyes played the numbers 4, 8, 15, 16, 23 and 42 and ended up winning the \$114-million jackpot. In real life, the lotto’s selections for its \$355-million prize — 4, 8, 15, 25, 47 and the crucial “Mega ball,” 42 — included four of Hurley’s numbers. According to the Mega Millions website, which reported receiving “unprecedented traffic” after the drawing, 41,763 people matched those four numbers, earning \$150 apiece.

Matching at least four numbers out of six is not that unlikely. Assuming there are 48 possible numbers in the lottery, and not bothering about specifics for this lottery like “Mega ball” and specific order, a basic probability computation for this match is

${6\choose 4}{44\choose 2}/{48\choose 6}=0.001156,$

that is a 1‰ chance when taking this lottery and this sequence of numbers in isolation. This probability does not account for the parallel and subsequent runs of many other lotteries where many players will have undoubtedly used those “lucky” numbers, since they seem to have been around for several years, nor for the fact that other series have also proposed lottery numbers (just a few weeks ago my daughter was watching an episode of the series Cold Case which involved a lottery draw).

### 6 Responses to “Another coincidence in lotteries”

1. [...] last week (here) 4 numbers (out of 6) appeared at the lottery in LA. As pointed out by Xian (here), the odds were not that small, i.e. it is a 1‰ [...]

2. Shouldn’t that read “that is a 0.1% chance when taking this lottery and this sequence of numbers in isolation.” ?

• Yes, this is what is written, using the permil symbol. Several people also got confused when I first used this symbol in an earlier lottery post!

• Got it now. I totally missed that extra o in the symbol! Thanks.

3. It would be interesting to know how many people bet oh Hurley’s numbers every week.

• Jean-Michel Marin asked me the same question when I told him the story! We would need to know the total number of players to see how far from a random variation away from the mean the actual number is.